{"id":1481,"date":"2023-12-06T10:19:18","date_gmt":"2023-12-06T15:19:18","guid":{"rendered":"https:\/\/matherealiser.fse.ulaval.ca\/?page_id=1481"},"modified":"2023-12-06T10:23:56","modified_gmt":"2023-12-06T15:23:56","slug":"manipulatives-for-numeracy","status":"publish","type":"page","link":"https:\/\/matherealiser.fse.ulaval.ca\/en\/manipulatives\/manipulatives-for-numeracy\/","title":{"rendered":"Manipulatives for numeracy"},"content":{"rendered":"\n<section class=\"wp-block-csrtcommun-gutenberg-block-bloc-strate  strate bg-undefined\" aria-label=\"\"><div class=\"strate-contenu\">\n<div class=\"wp-block-getwid-icon has-layout-framed\"><div class=\"wp-block-getwid-icon__wrapper has-text-color\" style=\"color:#f60404\"><i class=\"fas fa-cubes\"><\/i><\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading margin-top-20 accent margin-top-50\">Manipulatives for numeracy<\/h2>\n\n\n\n<p>In the progression of learning, three categories of equipment for working on numeracy are recognized: manipulatives with apparent and accessible groupings, manipulatives with apparent but non-accessible groupings, and manipulatives with non-apparent and non-accessible groupings. However, the different manipulatives also have other characteristics related to their relationship to writing, their relationship to the iconic, vocabulary, and the shape of the pieces.<\/p>\n\n\n\n<p>This page presents various manipulatives grouped according to the three categories of equipment prescribed in the learning progression. Under each photo of the manipulatives, some additional characteristics are presented, along with an interactive version that can be projected onto an interactive whiteboard. The characteristics presented correspond to those of the manipulatives based on its construction, not based on students&#8217; usage.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Manipulatives with apparent and accessible groupings<\/h3>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"771\" src=\"https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Centicubes-1-1024x771.jpg\" alt=\"\" class=\"wp-image-847\" style=\"object-fit:cover;width:252px;height:252px\" srcset=\"https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Centicubes-1-1024x771.jpg 1024w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Centicubes-1-300x226.jpg 300w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Centicubes-1-768x578.jpg 768w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Centicubes-1-1536x1157.jpg 1536w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Centicubes-1-2048x1542.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<div class=\"wp-block-getwid-accordion has-icon-left\" data-active-element=\"none\">\n<div class=\"wp-block-getwid-accordion__header-wrapper\"><span class=\"wp-block-getwid-accordion__header\"><a href=\"#\"><span class=\"wp-block-getwid-accordion__header-title\">Interlocking Cubes<\/span><span class=\"wp-block-getwid-accordion__icon is-active\"><i class=\"fas fa-plus\"><\/i><\/span><span class=\"wp-block-getwid-accordion__icon is-passive\"><i class=\"fas fa-minus\"><\/i><\/span><\/a><\/span><\/div><div class=\"wp-block-getwid-accordion__content-wrapper\"><div class=\"wp-block-getwid-accordion__content\">\n<ul class=\"wp-block-list\">\n<li>Open system.<\/li>\n\n\n\n<li>Metaphor : groupings.<\/li>\n\n\n\n<li>Counting required.<\/li>\n\n\n\n<li>No global recognition possible.<\/li>\n\n\n\n<li>Non-proportional model.<\/li>\n\n\n\n<li>The shape of the objects is identical.<\/li>\n\n\n\n<li>Vocabulary identical to the names of positions.<\/li>\n\n\n\n<li>Value does not depend on the organization of the material.<\/li>\n\n\n\n<li>Only one value for the same object.<\/li>\n\n\n\n<li>Drawing representation identical to the material.<\/li>\n<\/ul>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-csrtcommun-gutenberg-block-bloc-bouton-lien bouton-lien__wrapper  texte-left\"><a class=\"bouton-lien accent-blanc\" href=\"https:\/\/www.geogebra.org\/m\/ynnpazyd\">Interactive version<\/a><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"975\" src=\"https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Digi-blocks-1024x975.jpg\" alt=\"\" class=\"wp-image-822\" style=\"object-fit:cover;width:251px;height:251px\" srcset=\"https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Digi-blocks-1024x975.jpg 1024w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Digi-blocks-300x286.jpg 300w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Digi-blocks-768x731.jpg 768w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Digi-blocks-1536x1462.jpg 1536w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Digi-blocks-2048x1949.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<div class=\"wp-block-getwid-accordion has-icon-left\" data-active-element=\"none\">\n<div class=\"wp-block-getwid-accordion__header-wrapper\"><span class=\"wp-block-getwid-accordion__header\"><a href=\"#\"><span class=\"wp-block-getwid-accordion__header-title\">Digi-Blocks<\/span><span class=\"wp-block-getwid-accordion__icon is-active\"><i class=\"fas fa-plus\"><\/i><\/span><span class=\"wp-block-getwid-accordion__icon is-passive\"><i class=\"fas fa-minus\"><\/i><\/span><\/a><\/span><\/div><div class=\"wp-block-getwid-accordion__content-wrapper\"><div class=\"wp-block-getwid-accordion__content\">\n<ul class=\"wp-block-list\">\n<li>Closed system.<\/li>\n\n\n\n<li>Metaphor: packaging and unpacking.<\/li>\n\n\n\n<li>Counting not necessary.<\/li>\n\n\n\n<li>No global recognition possible.<\/li>\n\n\n\n<li>Proportional model.<\/li>\n\n\n\n<li>The shape of the objects is identical.<\/li>\n\n\n\n<li>Vocabulary identical to the names of positions.<\/li>\n\n\n\n<li>Value does not depend on the organization of the material.<\/li>\n\n\n\n<li>Only one value for the same object.<\/li>\n\n\n\n<li>Drawing representation different from the material (color and open boxes).<\/li>\n<\/ul>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-csrtcommun-gutenberg-block-bloc-bouton-lien bouton-lien__wrapper  texte-gauche\"><a class=\"bouton-lien accent-blanc\" href=\"https:\/\/www.geogebra.org\/m\/th5qmzyd\">Interactive version<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"771\" src=\"https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Jetons-1024x771.jpg\" alt=\"\" class=\"wp-image-834\" style=\"object-fit:cover;width:249px;height:249px\" srcset=\"https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Jetons-1024x771.jpg 1024w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Jetons-300x226.jpg 300w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Jetons-768x578.jpg 768w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Jetons-1536x1157.jpg 1536w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Jetons-2048x1542.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<div class=\"wp-block-getwid-accordion has-icon-left\" data-active-element=\"none\">\n<div class=\"wp-block-getwid-accordion__header-wrapper\"><span class=\"wp-block-getwid-accordion__header\"><a href=\"#\"><span class=\"wp-block-getwid-accordion__header-title\">Tokens<\/span><span class=\"wp-block-getwid-accordion__icon is-active\"><i class=\"fas fa-plus\"><\/i><\/span><span class=\"wp-block-getwid-accordion__icon is-passive\"><i class=\"fas fa-minus\"><\/i><\/span><\/a><\/span><\/div><div class=\"wp-block-getwid-accordion__content-wrapper\"><div class=\"wp-block-getwid-accordion__content\">\n<ul class=\"wp-block-list\">\n<li>Open system.<\/li>\n\n\n\n<li>Metaphor : groupings.<\/li>\n\n\n\n<li>Counting necessary.<\/li>\n\n\n\n<li>No global recognition possible.<\/li>\n\n\n\n<li>Non-proportional model.<\/li>\n\n\n\n<li>The shape of the objects is identical.<\/li>\n\n\n\n<li>Vocabulary identical to the names of positions.<\/li>\n\n\n\n<li>Value does not depend on the organization of the material.<\/li>\n\n\n\n<li>Only one value for the same object.<\/li>\n\n\n\n<li>Drawing representation identical to the material.<\/li>\n<\/ul>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-csrtcommun-gutenberg-block-bloc-bouton-lien bouton-lien__wrapper  texte-gauche\"><a class=\"bouton-lien accent-blanc\" href=\"https:\/\/www.geogebra.org\/m\/jba39jr3\">Interactive version<\/a><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"818\" src=\"https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Pates-alimentaires-1024x818.jpg\" alt=\"\" class=\"wp-image-837\" style=\"object-fit:cover;width:247px;height:247px\" srcset=\"https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Pates-alimentaires-1024x818.jpg 1024w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Pates-alimentaires-300x240.jpg 300w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Pates-alimentaires-768x614.jpg 768w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Pates-alimentaires-1536x1227.jpg 1536w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Pates-alimentaires-2048x1636.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<div class=\"wp-block-getwid-accordion has-icon-left\" data-active-element=\"none\">\n<div class=\"wp-block-getwid-accordion__header-wrapper\"><span class=\"wp-block-getwid-accordion__header\"><a href=\"#\"><span class=\"wp-block-getwid-accordion__header-title\">Pasta<\/span><span class=\"wp-block-getwid-accordion__icon is-active\"><i class=\"fas fa-plus\"><\/i><\/span><span class=\"wp-block-getwid-accordion__icon is-passive\"><i class=\"fas fa-minus\"><\/i><\/span><\/a><\/span><\/div><div class=\"wp-block-getwid-accordion__content-wrapper\"><div class=\"wp-block-getwid-accordion__content\">\n<ul class=\"wp-block-list\">\n<li>Open system.<\/li>\n\n\n\n<li>Metaphor: groupings.<\/li>\n\n\n\n<li>Counting necessary.<\/li>\n\n\n\n<li>No global recognition possible.<\/li>\n\n\n\n<li>Non-proportional model.<\/li>\n\n\n\n<li>The shape of the objects is identical.<\/li>\n\n\n\n<li>&nbsp;Vocabulary identical to the names of positions.<\/li>\n\n\n\n<li>Value does not depend on the organization of the material.<\/li>\n\n\n\n<li>Only one value for the same object.<\/li>\n\n\n\n<li>Drawing representation identical to the material.<\/li>\n<\/ul>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-csrtcommun-gutenberg-block-bloc-bouton-lien bouton-lien__wrapper  texte-gauche\"><a class=\"bouton-lien accent-blanc\" href=\"https:\/\/www.geogebra.org\/m\/yru2ws68\">Interactive version<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"826\" height=\"1024\" src=\"https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/10\/Boite-de-10-826x1024.jpeg\" alt=\"\" class=\"wp-image-1001\" style=\"object-fit:cover;width:243px;height:243px\" srcset=\"https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/10\/Boite-de-10-826x1024.jpeg 826w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/10\/Boite-de-10-242x300.jpeg 242w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/10\/Boite-de-10-768x952.jpeg 768w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/10\/Boite-de-10.jpeg 1028w\" sizes=\"auto, (max-width: 826px) 100vw, 826px\" \/><\/figure>\n\n\n\n<div class=\"wp-block-getwid-accordion has-icon-left\" data-active-element=\"none\">\n<div class=\"wp-block-getwid-accordion__header-wrapper\"><span class=\"wp-block-getwid-accordion__header\"><a href=\"#\"><span class=\"wp-block-getwid-accordion__header-title\">Box of 10<\/span><span class=\"wp-block-getwid-accordion__icon is-active\"><i class=\"fas fa-plus\"><\/i><\/span><span class=\"wp-block-getwid-accordion__icon is-passive\"><i class=\"fas fa-minus\"><\/i><\/span><\/a><\/span><\/div><div class=\"wp-block-getwid-accordion__content-wrapper\"><div class=\"wp-block-getwid-accordion__content\">\n<ul class=\"wp-block-list\">\n<li>Primarily used for supplements to 10.<\/li>\n\n\n\n<li>Counting not necessary.<\/li>\n\n\n\n<li>Global recognition possible.<\/li>\n\n\n\n<li>Only one value for the same object.<\/li>\n\n\n\n<li>Drawing representation identical to the material.<\/li>\n<\/ul>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-csrtcommun-gutenberg-block-bloc-bouton-lien bouton-lien__wrapper  texte-gauche\"><a class=\"bouton-lien accent-blanc\" href=\"https:\/\/www.mathlearningcenter.org\/apps\/number-frames\">Math Learning Center&#8217;s interactive version<\/a><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Manipulatives with apparent but non-accessible groupings<\/h3>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"711\" src=\"https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Base-10-1024x711.jpg\" alt=\"\" class=\"wp-image-866\" style=\"width:252px;height:190px\" srcset=\"https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Base-10-1024x711.jpg 1024w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Base-10-300x208.jpg 300w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Base-10-768x534.jpg 768w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Base-10-1536x1067.jpg 1536w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Base-10-2048x1423.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<div class=\"wp-block-getwid-accordion has-icon-left\" data-active-element=\"none\">\n<div class=\"wp-block-getwid-accordion__header-wrapper\"><span class=\"wp-block-getwid-accordion__header\"><a href=\"#\"><span class=\"wp-block-getwid-accordion__header-title\"><strong>Base 10 blocks<\/strong><\/span><span class=\"wp-block-getwid-accordion__icon is-active\"><i class=\"fas fa-plus\"><\/i><\/span><span class=\"wp-block-getwid-accordion__icon is-passive\"><i class=\"fas fa-minus\"><\/i><\/span><\/a><\/span><\/div><div class=\"wp-block-getwid-accordion__content-wrapper\"><div class=\"wp-block-getwid-accordion__content\">\n<ul class=\"wp-block-list\">\n<li>Open system.<\/li>\n\n\n\n<li>Metaphor: exchanges.<\/li>\n\n\n\n<li>Necessary counting.<\/li>\n\n\n\n<li>No global recognition possible.<\/li>\n\n\n\n<li>Proportional model.<\/li>\n\n\n\n<li>The shape of objects is variable.<\/li>\n\n\n\n<li>Vocabulary different from position names.<\/li>\n\n\n\n<li>Value does not depend on the organization of the material.<\/li>\n\n\n\n<li>The same object can only have one value.<\/li>\n\n\n\n<li>Representation in drawing identical to the material.<\/li>\n<\/ul>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-csrtcommun-gutenberg-block-bloc-bouton-lien bouton-lien__wrapper  texte-gauche\"><a class=\"bouton-lien accent-blanc\" href=\"https:\/\/www.mathlearningcenter.org\/apps\/number-pieces\">Math Learning Center&#8217;s interactive version<\/a><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"809\" src=\"https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/reglettes-1024x809.jpg\" alt=\"\" class=\"wp-image-925\" style=\"width:238px;height:188px\" srcset=\"https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/reglettes-1024x809.jpg 1024w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/reglettes-300x237.jpg 300w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/reglettes-768x606.jpg 768w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/reglettes-1536x1213.jpg 1536w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/reglettes-2048x1617.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<div class=\"wp-block-getwid-accordion has-icon-left\" data-active-element=\"none\">\n<div class=\"wp-block-getwid-accordion__header-wrapper\"><span class=\"wp-block-getwid-accordion__header\"><a href=\"#\"><span class=\"wp-block-getwid-accordion__header-title\"><strong>Rods<\/strong><\/span><span class=\"wp-block-getwid-accordion__icon is-active\"><i class=\"fas fa-plus\"><\/i><\/span><span class=\"wp-block-getwid-accordion__icon is-passive\"><i class=\"fas fa-minus\"><\/i><\/span><\/a><\/span><\/div><div class=\"wp-block-getwid-accordion__content-wrapper\"><div class=\"wp-block-getwid-accordion__content\">\n<ul class=\"wp-block-list\">\n<li>Open system.<\/li>\n\n\n\n<li>Metaphor : exchanges.<\/li>\n\n\n\n<li>Necessary counting.<\/li>\n\n\n\n<li>No global recognition possible.<\/li>\n\n\n\n<li>Proportional model.<\/li>\n\n\n\n<li>The shape of objects is variable.<\/li>\n\n\n\n<li>Vocabulary identical to position names.<\/li>\n\n\n\n<li>Value does not depend on the organization of the material.<\/li>\n\n\n\n<li>The same object can only have one value.<\/li>\n\n\n\n<li>Representation in drawing identical to the material.<\/li>\n<\/ul>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-csrtcommun-gutenberg-block-bloc-bouton-lien bouton-lien__wrapper  texte-gauche\"><a class=\"bouton-lien accent-blanc\" href=\"https:\/\/www.geogebra.org\/m\/janh5ecm\">Interactive version<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Manipulatives with non-apparent and non-accessible groupings<\/h3>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"734\" src=\"https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Abaque-1024x734.jpg\" alt=\"\" class=\"wp-image-870\" style=\"width:261px;height:196px\" srcset=\"https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Abaque-1024x734.jpg 1024w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Abaque-300x215.jpg 300w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Abaque-768x551.jpg 768w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Abaque-1536x1102.jpg 1536w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Abaque-2048x1469.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<div class=\"wp-block-getwid-accordion has-icon-left\" data-active-element=\"none\">\n<div class=\"wp-block-getwid-accordion__header-wrapper\"><span class=\"wp-block-getwid-accordion__header\"><a href=\"#\"><span class=\"wp-block-getwid-accordion__header-title\">Abacus<\/span><span class=\"wp-block-getwid-accordion__icon is-active\"><i class=\"fas fa-plus\"><\/i><\/span><span class=\"wp-block-getwid-accordion__icon is-passive\"><i class=\"fas fa-minus\"><\/i><\/span><\/a><\/span><\/div><div class=\"wp-block-getwid-accordion__content-wrapper\"><div class=\"wp-block-getwid-accordion__content\">\n<ul class=\"wp-block-list\">\n<li>Open system.<\/li>\n\n\n\n<li>Metaphor: exchanges.<\/li>\n\n\n\n<li>Necessary counting.<\/li>\n\n\n\n<li>No global recognition possible.<\/li>\n\n\n\n<li>Non-proportional model.<\/li>\n\n\n\n<li>The shape of objects is identical.<\/li>\n\n\n\n<li>Vocabulary identical to position names.<\/li>\n\n\n\n<li>Value depends on the organization of the material.<\/li>\n\n\n\n<li>The same object can only have one value.<\/li>\n\n\n\n<li>Representation in drawing identical to the material.<\/li>\n<\/ul>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-csrtcommun-gutenberg-block-bloc-bouton-lien bouton-lien__wrapper  texte-gauche\"><a class=\"bouton-lien accent-blanc\" href=\"https:\/\/www.geogebra.org\/m\/gysfmggr\">Interactive version<\/a><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"993\" height=\"1024\" src=\"https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Rek-N-Rek-993x1024.jpg\" alt=\"\" class=\"wp-image-928\" style=\"width:206px;height:197px\" srcset=\"https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Rek-N-Rek-993x1024.jpg 993w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Rek-N-Rek-291x300.jpg 291w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Rek-N-Rek-768x792.jpg 768w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Rek-N-Rek-1489x1536.jpg 1489w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Rek-N-Rek-1986x2048.jpg 1986w\" sizes=\"auto, (max-width: 993px) 100vw, 993px\" \/><\/figure>\n\n\n\n<div class=\"wp-block-getwid-accordion has-icon-left\" data-active-element=\"none\">\n<div class=\"wp-block-getwid-accordion__header-wrapper\"><span class=\"wp-block-getwid-accordion__header\"><a href=\"#\"><span class=\"wp-block-getwid-accordion__header-title\">Rekenrek<\/span><span class=\"wp-block-getwid-accordion__icon is-active\"><i class=\"fas fa-plus\"><\/i><\/span><span class=\"wp-block-getwid-accordion__icon is-passive\"><i class=\"fas fa-minus\"><\/i><\/span><\/a><\/span><\/div><div class=\"wp-block-getwid-accordion__content-wrapper\"><div class=\"wp-block-getwid-accordion__content\">\n<ul class=\"wp-block-list\">\n<li>Open system.<\/li>\n\n\n\n<li>Metaphor: exchanges.<\/li>\n\n\n\n<li>Necessary counting.<\/li>\n\n\n\n<li>No global recognition possible.<\/li>\n\n\n\n<li>Non-proportional model.<\/li>\n\n\n\n<li>The shape of objects is identical.<\/li>\n\n\n\n<li>Value depends on the organization of the material.<\/li>\n\n\n\n<li>The same object can only have one value.<\/li>\n\n\n\n<li>Representation in drawing identical to the material.<\/li>\n<\/ul>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-csrtcommun-gutenberg-block-bloc-bouton-lien bouton-lien__wrapper  texte-gauche\"><a class=\"bouton-lien accent-blanc\" href=\"https:\/\/www.mathlearningcenter.org\/apps\/number-rack\">Math Learning Center&#8217;s interactive version<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"863\" src=\"https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Abaque-maison-1024x863.jpg\" alt=\"\" class=\"wp-image-874\" style=\"width:280px;height:211px\" srcset=\"https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Abaque-maison-1024x863.jpg 1024w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Abaque-maison-300x253.jpg 300w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Abaque-maison-768x647.jpg 768w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Abaque-maison-1536x1294.jpg 1536w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Abaque-maison-2048x1726.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<div class=\"wp-block-getwid-accordion has-icon-left\" data-active-element=\"none\">\n<div class=\"wp-block-getwid-accordion__header-wrapper\"><span class=\"wp-block-getwid-accordion__header\"><a href=\"#\"><span class=\"wp-block-getwid-accordion__header-title\">House Abacus<\/span><span class=\"wp-block-getwid-accordion__icon is-active\"><i class=\"fas fa-plus\"><\/i><\/span><span class=\"wp-block-getwid-accordion__icon is-passive\"><i class=\"fas fa-minus\"><\/i><\/span><\/a><\/span><\/div><div class=\"wp-block-getwid-accordion__content-wrapper\"><div class=\"wp-block-getwid-accordion__content\">\n<ul class=\"wp-block-list\">\n<li>Open system.<\/li>\n\n\n\n<li>Metaphor : exchanges.<\/li>\n\n\n\n<li>Necessary counting.<\/li>\n\n\n\n<li>No global recognition possible.<\/li>\n\n\n\n<li>Non-proportional model.<\/li>\n\n\n\n<li>The shape of objects is identical.<\/li>\n\n\n\n<li>Vocabulary identical to position names.<\/li>\n\n\n\n<li>Value depends on the organization of the material.<\/li>\n\n\n\n<li>The same object can have multiple values.<\/li>\n\n\n\n<li>Representation in drawing identical to the material.<\/li>\n<\/ul>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-csrtcommun-gutenberg-block-bloc-bouton-lien bouton-lien__wrapper  texte-gauche\"><a class=\"bouton-lien accent-blanc\" href=\"https:\/\/www.geogebra.org\/m\/fjrumctw\">Interactive version<\/a><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"771\" src=\"https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Abaque-triangulaire-1024x771.jpg\" alt=\"\" class=\"wp-image-876\" style=\"width:222px;height:210px\" srcset=\"https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Abaque-triangulaire-1024x771.jpg 1024w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Abaque-triangulaire-300x226.jpg 300w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Abaque-triangulaire-768x578.jpg 768w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Abaque-triangulaire-1536x1157.jpg 1536w, https:\/\/matherealiser.fse.ulaval.ca\/wp-content\/uploads\/sites\/13\/2023\/09\/Abaque-triangulaire-2048x1542.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<div class=\"wp-block-getwid-accordion has-icon-left\" data-active-element=\"none\">\n<div class=\"wp-block-getwid-accordion__header-wrapper\"><span class=\"wp-block-getwid-accordion__header\"><a href=\"#\"><span class=\"wp-block-getwid-accordion__header-title\">Triangular-house abacus<\/span><span class=\"wp-block-getwid-accordion__icon is-active\"><i class=\"fas fa-plus\"><\/i><\/span><span class=\"wp-block-getwid-accordion__icon is-passive\"><i class=\"fas fa-minus\"><\/i><\/span><\/a><\/span><\/div><div class=\"wp-block-getwid-accordion__content-wrapper\"><div class=\"wp-block-getwid-accordion__content\">\n<ul class=\"wp-block-list\">\n<li>Open system.<\/li>\n\n\n\n<li>Metaphor: exchanges.<\/li>\n\n\n\n<li>Counting not necessary.<\/li>\n\n\n\n<li>No global recognition possible.<\/li>\n\n\n\n<li>Non-proportional model.<\/li>\n\n\n\n<li>The shape of objects is identical.<\/li>\n\n\n\n<li>Vocabulary identical to position names.<\/li>\n\n\n\n<li>Value depends on the organization of the material.<\/li>\n\n\n\n<li>The same object can have multiple values.<\/li>\n\n\n\n<li>Representation in drawing identical to the material.<\/li>\n<\/ul>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-csrtcommun-gutenberg-block-bloc-bouton-lien bouton-lien__wrapper  texte-gauche\"><a class=\"bouton-lien accent-blanc\" href=\"https:\/\/www.geogebra.org\/m\/vtnkhdbx\">Interactive version<\/a><\/div>\n<\/div>\n<\/div>\n<div class=\"clearFix\"><\/div><\/div><\/section>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":67,"featured_media":0,"parent":1479,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"page-secondaire-pleine-page.php","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-1481","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/matherealiser.fse.ulaval.ca\/en\/wp-json\/wp\/v2\/pages\/1481","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/matherealiser.fse.ulaval.ca\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/matherealiser.fse.ulaval.ca\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/matherealiser.fse.ulaval.ca\/en\/wp-json\/wp\/v2\/users\/67"}],"replies":[{"embeddable":true,"href":"https:\/\/matherealiser.fse.ulaval.ca\/en\/wp-json\/wp\/v2\/comments?post=1481"}],"version-history":[{"count":9,"href":"https:\/\/matherealiser.fse.ulaval.ca\/en\/wp-json\/wp\/v2\/pages\/1481\/revisions"}],"predecessor-version":[{"id":1562,"href":"https:\/\/matherealiser.fse.ulaval.ca\/en\/wp-json\/wp\/v2\/pages\/1481\/revisions\/1562"}],"up":[{"embeddable":true,"href":"https:\/\/matherealiser.fse.ulaval.ca\/en\/wp-json\/wp\/v2\/pages\/1479"}],"wp:attachment":[{"href":"https:\/\/matherealiser.fse.ulaval.ca\/en\/wp-json\/wp\/v2\/media?parent=1481"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}