{"id":47,"date":"2023-01-25T16:33:56","date_gmt":"2023-01-25T16:33:56","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/early-counting-systems-dig-deeper-page-1\/"},"modified":"2024-10-18T20:52:28","modified_gmt":"2024-10-18T20:52:28","slug":"early-counting-systems-fresh-take","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/early-counting-systems-fresh-take\/","title":{"raw":"Early Counting Systems: Fresh Take","rendered":"Early Counting Systems: Fresh Take"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Understand early counting systems and their representation of numbers<\/li>\r\n\t<li>Recognize the chronological order of counting system development<\/li>\r\n\t<li>Convert Hindu-Arabic and Roman Numerals<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Counting Boards<\/h2>\r\n<section class=\"textbox watchIt\"><iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/fL1N_V89g78\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Inca+Counting+Boards.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cInca Counting Boards\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<section class=\"textbox seeExample\">Suppose you have the following counting board with two different kind of pebbles places as illustrated. Let the solid black pebble represent a dog and the striped pebble represent a cat.\r\n\r\n\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n\t<li>How many dogs are being represented?<\/li>\r\n\t<li>How many cats are represented on this board?<\/li>\r\n<\/ol>\r\n<center><img class=\"alignnone wp-image-283 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/282\/2016\/01\/20155151\/Fig5_1_4.png\" alt=\"Simple depiction of an Incan counting board. There are two black pebbles and one striped pebble in the outer square regions. There are three black pebbles and no striped pebbles in the larger white rectangular compartments. There is one black pebble and six striped pebbles in the middle region. There are three black pebbles and three striped pebbles on the second levels. Finally, there is one black pebble and two striped pebbles on the highest corner levels.\" width=\"474\" height=\"311\" \/><\/center><br \/>\r\n<p>&nbsp;<\/p>\r\n\r\n\r\n[reveal-answer q=\"129586\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"129586\"]\r\n\r\n\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n\t<li>There are two black pebbles in the outer square regions - these represent [latex]2[\/latex] dogs.\u00a0There are three black pebbles in the larger (white) rectangular compartments - these represent [latex]6[\/latex] dogs.\u00a0There is one black pebble in the middle region - this represents [latex]3[\/latex] dogs.\u00a0There are three black pebbles on the second level - these represent [latex]18[\/latex] dogs.\u00a0Finally, there is one black pebble on the highest corner level - this represents [latex]12[\/latex] dogs. We then have a total of [latex]2+6+3+18+12 = 41[\/latex] dogs.<\/li>\r\n\t<li>There is one striped pebble in the outer square regions - these represent [latex]1[\/latex] cat. There are [latex]6[\/latex] striped pebbles in the middle region - this represents [latex]18[\/latex] dogs. There are three striped pebbles on the second level - these represent [latex]18[\/latex] cats. Finally, there are two striped pebbles on the highest corner level - this represents [latex]24[\/latex] cats.We then have a total of [latex]1+18+18+24 = 61[\/latex] cats.<\/li>\r\n<\/ol>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<h2>The Quipu<\/h2>\r\n<section class=\"textbox watchIt\"><iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/OFbbiAf8kUo\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Inca+Knot+Numbers+-+Numberphile.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cInca Knot Numbers - Numberphile\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<section class=\"textbox watchIt\"><iframe title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/EYq-VtyAd2s\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\r\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/The+Inca+Quipu.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cThe Inca Quipu\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2292[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2290[\/ohm2_question]<\/section>\r\n<h2>The Hindu\u2014Arabic Number System and Roman Numerals<\/h2>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2329[\/ohm2_question]<\/section>\r\n<section class=\"textbox watchIt\"><iframe src=\"\/\/plugin.3playmedia.com\/show?mf=10371501&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=vAmCV_lEqsc&amp;video_target=tpm-plugin-7em26oyg-vAmCV_lEqsc\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe><br \/>\r\n<p>You can view the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Roman+Numerals.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cRoman Numerals\u201d here (opens in new window).<\/a><\/p>\r\n<\/section>\r\n<section class=\"textbox seeExample\">Write the Hindu-Arabic numeral for [latex]MCMIV[\/latex].<br \/>\r\n[reveal-answer q=\"129583\"]Show Solution[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"129583\"]One thousand nine hundred four, [latex]1904[\/latex] ([latex]M[\/latex] is a thousand, [latex]CM[\/latex] is nine hundred and [latex]IV[\/latex] is four).[\/hidden-answer]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2326[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Understand early counting systems and their representation of numbers<\/li>\n<li>Recognize the chronological order of counting system development<\/li>\n<li>Convert Hindu-Arabic and Roman Numerals<\/li>\n<\/ul>\n<\/section>\n<h2>Counting Boards<\/h2>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/fL1N_V89g78\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Inca+Counting+Boards.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cInca Counting Boards\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<section class=\"textbox seeExample\">Suppose you have the following counting board with two different kind of pebbles places as illustrated. Let the solid black pebble represent a dog and the striped pebble represent a cat.<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>How many dogs are being represented?<\/li>\n<li>How many cats are represented on this board?<\/li>\n<\/ol>\n<div style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-283 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/282\/2016\/01\/20155151\/Fig5_1_4.png\" alt=\"Simple depiction of an Incan counting board. There are two black pebbles and one striped pebble in the outer square regions. There are three black pebbles and no striped pebbles in the larger white rectangular compartments. There is one black pebble and six striped pebbles in the middle region. There are three black pebbles and three striped pebbles on the second levels. Finally, there is one black pebble and two striped pebbles on the highest corner levels.\" width=\"474\" height=\"311\" \/><\/div>\n<div class=\"wp-nocaption \"><\/div>\n<p>&nbsp;<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q129586\">Show Solution<\/button><\/p>\n<div id=\"q129586\" class=\"hidden-answer\" style=\"display: none\">\n<ol style=\"list-style-type: lower-alpha;\">\n<li>There are two black pebbles in the outer square regions &#8211; these represent [latex]2[\/latex] dogs.\u00a0There are three black pebbles in the larger (white) rectangular compartments &#8211; these represent [latex]6[\/latex] dogs.\u00a0There is one black pebble in the middle region &#8211; this represents [latex]3[\/latex] dogs.\u00a0There are three black pebbles on the second level &#8211; these represent [latex]18[\/latex] dogs.\u00a0Finally, there is one black pebble on the highest corner level &#8211; this represents [latex]12[\/latex] dogs. We then have a total of [latex]2+6+3+18+12 = 41[\/latex] dogs.<\/li>\n<li>There is one striped pebble in the outer square regions &#8211; these represent [latex]1[\/latex] cat. There are [latex]6[\/latex] striped pebbles in the middle region &#8211; this represents [latex]18[\/latex] dogs. There are three striped pebbles on the second level &#8211; these represent [latex]18[\/latex] cats. Finally, there are two striped pebbles on the highest corner level &#8211; this represents [latex]24[\/latex] cats.We then have a total of [latex]1+18+18+24 = 61[\/latex] cats.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/section>\n<h2>The Quipu<\/h2>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/OFbbiAf8kUo\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Inca+Knot+Numbers+-+Numberphile.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cInca Knot Numbers &#8211; Numberphile\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/EYq-VtyAd2s\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>You can view the\u00a0<a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/The+Inca+Quipu.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cThe Inca Quipu\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2292\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2292&theme=lumen&iframe_resize_id=ohm2292&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2290\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2290&theme=lumen&iframe_resize_id=ohm2290&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<h2>The Hindu\u2014Arabic Number System and Roman Numerals<\/h2>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2329\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2329&theme=lumen&iframe_resize_id=ohm2329&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox watchIt\"><iframe loading=\"lazy\" src=\"\/\/plugin.3playmedia.com\/show?mf=10371501&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=vAmCV_lEqsc&amp;video_target=tpm-plugin-7em26oyg-vAmCV_lEqsc\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe><\/p>\n<p>You can view the <a href=\"https:\/\/course-building.s3.us-west-2.amazonaws.com\/Quantitative+Reasoning+-+2023+Build\/Transcriptions\/Roman+Numerals.txt\" target=\"_blank\" rel=\"noopener\">transcript for \u201cRoman Numerals\u201d here (opens in new window).<\/a><\/p>\n<\/section>\n<section class=\"textbox seeExample\">Write the Hindu-Arabic numeral for [latex]MCMIV[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q129583\">Show Solution<\/button><\/p>\n<div id=\"q129583\" class=\"hidden-answer\" style=\"display: none\">One thousand nine hundred four, [latex]1904[\/latex] ([latex]M[\/latex] is a thousand, [latex]CM[\/latex] is nine hundred and [latex]IV[\/latex] is four).<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2326\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2326&theme=lumen&iframe_resize_id=ohm2326&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":15,"menu_order":11,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Math in Society\",\"author\":\"Lippman, David\",\"organization\":\"\",\"url\":\"http:\/\/www.opentextbookstore.com\/mathinsociety\/\",\"project\":\"\",\"license\":\"cc-by-sa\",\"license_terms\":\"\"}]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":40,"module-header":"fresh_take","content_attributions":[{"type":"original","description":"Revision and Adaptation","author":"","organization":"Lumen Learning","url":"","project":"","license":"cc-by","license_terms":""},{"type":"cc","description":"Math in Society","author":"Lippman, 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