{"id":298,"date":"2020-10-10T14:43:41","date_gmt":"2020-10-10T12:43:41","guid":{"rendered":"http:\/\/eduhm.fr\/?page_id=298"},"modified":"2022-04-27T12:27:46","modified_gmt":"2022-04-27T10:27:46","slug":"6e-numeration-quipous-incas","status":"publish","type":"page","link":"http:\/\/eduhm.fr\/?page_id=298","title":{"rendered":"6e num\u00e9ration Quipous incas"},"content":{"rendered":"\n<p>R\u00e9alis\u00e9e aupr\u00e8s de deux classes de 6e \u00e0 l\u2019occasion de la Semaine des Math\u00e9matiques, cette s\u00e9ance est un travail sur la num\u00e9ration \u00e0 partir de la lecture et la r\u00e9alisation de quipous incas.<\/p>\n\n\n\n<p>Cette s\u00e9ance constitue une tentative d\u2019articulation entre une pratique de num\u00e9ration ancienne et l\u2019\u00e9clairage de travaux de didactique sur le sujet math\u00e9matique abord\u00e9. Dans le cas pr\u00e9sent, l\u2019\u00e9vocation des grands nombres \u00e0 partir des quipus est mis dans la perspective de la distinction unit\u00e9s\/classes de Fr\u00e9d\u00e9ric Tempier(*). Tout au long de la s\u00e9ance, le travail s\u2019organise donc autour du r\u00f4le de trois quipus distincts, le premier pour la classe des unit\u00e9s, le second pour celle des milliers, et le troisi\u00e8me pour celle des millions.<\/p>\n\n\n\n<p>Fiche \u00e9l\u00e8ve :&nbsp;<a href=\"http:\/\/eduhm.fr\/wp-content\/uploads\/2020\/10\/6_quipou_fiche.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">6_quipou_fiche<\/a><\/p>\n\n\n\n<p>A consulter :<\/p>\n\n\n\n<p>Site internet de Fr\u00e9d\u00e9ric Tempier :&nbsp;<a href=\"http:\/\/numerationdecimale.free.fr\/\" target=\"_blank\" rel=\"noreferrer noopener\">numerationdecimale.free.fr<\/a><\/p>\n\n\n\n<p><em>Niveau : sixi\u00e8me \/ Ann\u00e9e 2014<\/em><\/p>\n\n\n\n<p>Une analyse d\u00e9taill\u00e9e de cette s\u00e9ance est propos\u00e9e dans l\u2019article \u00ab Travailler la num\u00e9ration d\u00e9cimale avec les quipus incas : bienfaits et limites autour d\u2019une exp\u00e9rimentation en classe de sixi\u00e8me \u00bb, De Vittori &amp; Leroy,\u00a0<em>Rep\u00e8res-IREM<\/em>, n\u00b0107, 2017.<\/p>\n\n\n\n<p><strong>Extrait 1 : Premier contact avec les quipus<\/strong><\/p>\n\n\n\n<p>Apr\u00e8s une pr\u00e9sentation du contexte historique et du r\u00f4le des quipus comme outils pour conserver la m\u00e9moire des quantit\u00e9s, les \u00e9l\u00e8ves s\u2019entrainent \u00e0 \u00ab&nbsp;lire&nbsp;\u00bb un quipu donn\u00e9. Le nombre choisi (436) permet de r\u00e9activer la valeur des chiffres selon leur position et le vocabulaire associ\u00e9.<\/p>\n\n\n<div class=\"passster-form\" id=\"ps-383\">  \n  <form class=\"password-form\" method=\"post\" autocomplete=\"off\" action-xhr=\"http:\/\/eduhm.fr\/?page_id=298\" target=\"_top\">\n    <h4>Protected Area<\/h4>\n    <p>This content is password-protected. Please verify with a password to unlock the content.<\/p>\n    <fieldset>\n      <span class=\"ps-loader\"><img src=\"http:\/\/eduhm.fr\/wp-content\/plugins\/content-protector\/assets\/public\/ps-loader.svg\"\/><\/span>\n      <input placeholder=\"Enter your password..\" type=\"password\" tabindex=\"1\" name=\"passster_password\" id=\"passster_password\" class=\"passster-password\" autocomplete=\"off\" data-protection-type=\"password\" data-list=\"[PASSSTER_LIST]\" data-area=\"[PASSSTER_AREA]\" data-protection=\"[PASSSTER_PROTECTION]\">\n      \n      <button name=\"submit\" type=\"submit\" class=\"passster-submit\" data-psid=\"ps-383\"  data-submit=\"...Checking Password\">Saisissez le mot de passe pour acc\u00e9der \u00e0 la vid\u00e9o<\/button>\n       <div class=\"passster-error\"><\/div>\n    <\/fieldset>\n  <\/form>\n<\/div>\n\n\n<p><strong>Extrait 2 : Des n\u0153uds sur des cordes<\/strong><\/p>\n\n\n\n<p>La r\u00e9alisation des n\u0153uds n\u2019est pas si simple\u2026<\/p>\n\n\n\n<p><em>Remarque : il est pr\u00e9f\u00e9rable de choisir une cordelette en mati\u00e8re synth\u00e9tique afin d\u2019\u00e9viter l\u2019effilochage et de permet de d\u00e9faire les n\u0153uds facilement.<\/em><\/p>\n\n\n<div class=\"passster-form\" id=\"ps-64\">  \n  <form class=\"password-form\" method=\"post\" autocomplete=\"off\" action-xhr=\"http:\/\/eduhm.fr\/?page_id=298\" target=\"_top\">\n    <h4>Protected Area<\/h4>\n    <p>This content is password-protected. Please verify with a password to unlock the content.<\/p>\n    <fieldset>\n      <span class=\"ps-loader\"><img src=\"http:\/\/eduhm.fr\/wp-content\/plugins\/content-protector\/assets\/public\/ps-loader.svg\"\/><\/span>\n      <input placeholder=\"Enter your password..\" type=\"password\" tabindex=\"1\" name=\"passster_password\" id=\"passster_password\" class=\"passster-password\" autocomplete=\"off\" data-protection-type=\"password\" data-list=\"[PASSSTER_LIST]\" data-area=\"[PASSSTER_AREA]\" data-protection=\"[PASSSTER_PROTECTION]\">\n      \n      <button name=\"submit\" type=\"submit\" class=\"passster-submit\" data-psid=\"ps-64\"  data-submit=\"...Checking Password\">Saisissez le mot de passe pour acc\u00e9der \u00e0 la vid\u00e9o<\/button>\n       <div class=\"passster-error\"><\/div>\n    <\/fieldset>\n  <\/form>\n<\/div>\n\n\n<p><strong>Extrait 3 : Un chiffre \u2013 un noeud<\/strong><\/p>\n\n\n\n<p>R\u00e9alisation d\u2019un quipu impos\u00e9 (461) et identification du principe de construction semblable \u00e0 notre syst\u00e8me de num\u00e9ration : un n\u0153ud pour chaque rang.<\/p>\n\n\n<div class=\"passster-form\" id=\"ps-525\">  \n  <form class=\"password-form\" method=\"post\" autocomplete=\"off\" action-xhr=\"http:\/\/eduhm.fr\/?page_id=298\" target=\"_top\">\n    <h4>Protected Area<\/h4>\n    <p>This content is password-protected. Please verify with a password to unlock the content.<\/p>\n    <fieldset>\n      <span class=\"ps-loader\"><img src=\"http:\/\/eduhm.fr\/wp-content\/plugins\/content-protector\/assets\/public\/ps-loader.svg\"\/><\/span>\n      <input placeholder=\"Enter your password..\" type=\"password\" tabindex=\"1\" name=\"passster_password\" id=\"passster_password\" class=\"passster-password\" autocomplete=\"off\" data-protection-type=\"password\" data-list=\"[PASSSTER_LIST]\" data-area=\"[PASSSTER_AREA]\" data-protection=\"[PASSSTER_PROTECTION]\">\n      \n      <button name=\"submit\" type=\"submit\" class=\"passster-submit\" data-psid=\"ps-525\"  data-submit=\"...Checking Password\">Saisissez le mot de passe pour acc\u00e9der \u00e0 la vid\u00e9o<\/button>\n       <div class=\"passster-error\"><\/div>\n    <\/fieldset>\n  <\/form>\n<\/div>\n\n\n<p><strong>Extrait 4 : Aller au-del\u00e0 de 999<\/strong><\/p>\n\n\n\n<p>L\u2019\u00e9criture de grands nombres \u00e0 l\u2019aide de quipus est l\u2019occasion de revoir la n\u00e9cessit\u00e9 de les s\u00e9parer en blocs de trois chiffres correspondant respectivement aux unit\u00e9s, milliers et millions.<\/p>\n\n\n<div class=\"passster-form\" id=\"ps-264\">  \n  <form class=\"password-form\" method=\"post\" autocomplete=\"off\" action-xhr=\"http:\/\/eduhm.fr\/?page_id=298\" target=\"_top\">\n    <h4>Protected Area<\/h4>\n    <p>This content is password-protected. Please verify with a password to unlock the content.<\/p>\n    <fieldset>\n      <span class=\"ps-loader\"><img src=\"http:\/\/eduhm.fr\/wp-content\/plugins\/content-protector\/assets\/public\/ps-loader.svg\"\/><\/span>\n      <input placeholder=\"Enter your password..\" type=\"password\" tabindex=\"1\" name=\"passster_password\" id=\"passster_password\" class=\"passster-password\" autocomplete=\"off\" data-protection-type=\"password\" data-list=\"[PASSSTER_LIST]\" data-area=\"[PASSSTER_AREA]\" data-protection=\"[PASSSTER_PROTECTION]\">\n      \n      <button name=\"submit\" type=\"submit\" class=\"passster-submit\" data-psid=\"ps-264\"  data-submit=\"...Checking Password\">Saisissez le mot de passe pour acc\u00e9der \u00e0 la vid\u00e9o<\/button>\n       <div class=\"passster-error\"><\/div>\n    <\/fieldset>\n  <\/form>\n<\/div>\n\n\n<p><strong>Extrait 5 : Lecture d\u2019un \u00ab&nbsp;grand&nbsp;\u00bb quipu inconnu<\/strong><\/p>\n\n\n\n<p>Chaque groupe d\u2019\u00e9l\u00e8ves a r\u00e9alis\u00e9 un quipu correspondant \u00e0 un nombre sup\u00e9rieur \u00e0 un million. Les diff\u00e9rents quipus circulent alors de groupe en groupe afin d\u2019\u00eatre lus ce qui permet de bien distinguer les cordes des unit\u00e9s, des milliers et des millions et les n\u0153uds des unit\u00e9s, dizaines et centaines qui y apparaissent. Le choix des nombres permet de commencer \u00e0 mettre en \u00e9vidence l\u2019absence de marqueur pour le z\u00e9ro.<\/p>\n\n\n<div class=\"passster-form\" id=\"ps-469\">  \n  <form class=\"password-form\" method=\"post\" autocomplete=\"off\" action-xhr=\"http:\/\/eduhm.fr\/?page_id=298\" target=\"_top\">\n    <h4>Protected Area<\/h4>\n    <p>This content is password-protected. Please verify with a password to unlock the content.<\/p>\n    <fieldset>\n      <span class=\"ps-loader\"><img src=\"http:\/\/eduhm.fr\/wp-content\/plugins\/content-protector\/assets\/public\/ps-loader.svg\"\/><\/span>\n      <input placeholder=\"Enter your password..\" type=\"password\" tabindex=\"1\" name=\"passster_password\" id=\"passster_password\" class=\"passster-password\" autocomplete=\"off\" data-protection-type=\"password\" data-list=\"[PASSSTER_LIST]\" data-area=\"[PASSSTER_AREA]\" data-protection=\"[PASSSTER_PROTECTION]\">\n      \n      <button name=\"submit\" type=\"submit\" class=\"passster-submit\" data-psid=\"ps-469\"  data-submit=\"...Checking Password\">Saisissez le mot de passe pour acc\u00e9der \u00e0 la vid\u00e9o<\/button>\n       <div class=\"passster-error\"><\/div>\n    <\/fieldset>\n  <\/form>\n<\/div>\n\n\n<p><strong>Extrait 6 : Bilan<\/strong><\/p>\n\n\n\n<p>La synth\u00e8se de l\u2019activit\u00e9 est l\u2019occasion de revenir sur l\u2019importance de la place du chiffre dans l\u2019\u00e9criture. Ici, en fin d\u2019extrait, un groupe n\u2019a pas correctement plac\u00e9 le n\u0153ud des unit\u00e9s de millions ce qui a entrain\u00e9 un \u00e9cart avec ce que les \u00e9l\u00e8ves des autres groupes ont pu lire.<\/p>\n\n\n<div class=\"passster-form\" id=\"ps-557\">  \n  <form class=\"password-form\" method=\"post\" autocomplete=\"off\" action-xhr=\"http:\/\/eduhm.fr\/?page_id=298\" target=\"_top\">\n    <h4>Protected Area<\/h4>\n    <p>This content is password-protected. Please verify with a password to unlock the content.<\/p>\n    <fieldset>\n      <span class=\"ps-loader\"><img src=\"http:\/\/eduhm.fr\/wp-content\/plugins\/content-protector\/assets\/public\/ps-loader.svg\"\/><\/span>\n      <input placeholder=\"Enter your password..\" type=\"password\" tabindex=\"1\" name=\"passster_password\" id=\"passster_password\" class=\"passster-password\" autocomplete=\"off\" data-protection-type=\"password\" data-list=\"[PASSSTER_LIST]\" data-area=\"[PASSSTER_AREA]\" data-protection=\"[PASSSTER_PROTECTION]\">\n      \n      <button name=\"submit\" type=\"submit\" class=\"passster-submit\" data-psid=\"ps-557\"  data-submit=\"...Checking Password\">Saisissez le mot de passe pour acc\u00e9der \u00e0 la vid\u00e9o<\/button>\n       <div class=\"passster-error\"><\/div>\n    <\/fieldset>\n  <\/form>\n<\/div>\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>R\u00e9alis\u00e9e aupr\u00e8s de deux classes de 6e \u00e0 l\u2019occasion de la Semaine des Math\u00e9matiques, cette s\u00e9ance est un travail sur la num\u00e9ration \u00e0 partir de la lecture et la r\u00e9alisation de quipous incas. Cette s\u00e9ance constitue une tentative d\u2019articulation entre une pratique de num\u00e9ration ancienne et l\u2019\u00e9clairage de travaux de didactique sur le sujet math\u00e9matique &hellip; <\/p>\n<p class=\"link-more\"><a href=\"http:\/\/eduhm.fr\/?page_id=298\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;6e num\u00e9ration Quipous incas&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"http:\/\/eduhm.fr\/index.php?rest_route=\/wp\/v2\/pages\/298"}],"collection":[{"href":"http:\/\/eduhm.fr\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/eduhm.fr\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/eduhm.fr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/eduhm.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=298"}],"version-history":[{"count":8,"href":"http:\/\/eduhm.fr\/index.php?rest_route=\/wp\/v2\/pages\/298\/revisions"}],"predecessor-version":[{"id":434,"href":"http:\/\/eduhm.fr\/index.php?rest_route=\/wp\/v2\/pages\/298\/revisions\/434"}],"wp:attachment":[{"href":"http:\/\/eduhm.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=298"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}