{"id":259,"date":"2024-08-22T19:17:35","date_gmt":"2024-08-22T19:17:35","guid":{"rendered":"https:\/\/learnx.ca\/mt\/?page_id=259"},"modified":"2025-12-06T12:20:17","modified_gmt":"2025-12-06T12:20:17","slug":"infinity-overview","status":"publish","type":"page","link":"https:\/\/learnx.ca\/mt\/","title":{"rendered":"4. Infinity in your Hand"},"content":{"rendered":"\n<h4 class=\"wp-block-heading\">placemat<\/h4>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"625\" height=\"482\" src=\"https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/infinity-1-v2.png\" alt=\"\" class=\"wp-image-425\" style=\"width:684px;height:auto\" srcset=\"https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/infinity-1-v2.png 625w, https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/infinity-1-v2-300x231.png 300w\" sizes=\"auto, (max-width: 625px) 85vw, 625px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>placemat Tasks<\/strong><\/h4>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"966\" height=\"744\" src=\"https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/MT1-4-prompts.png\" alt=\"\" class=\"wp-image-269\" style=\"width:688px;height:auto\" srcset=\"https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/MT1-4-prompts.png 966w, https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/MT1-4-prompts-300x231.png 300w, https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/MT1-4-prompts-768x592.png 768w\" sizes=\"auto, (max-width: 709px) 85vw, (max-width: 909px) 67vw, (max-width: 1362px) 62vw, 840px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>IN THE CLASSROOM<\/strong><\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"alignright size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"160\" height=\"140\" src=\"https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/infinity-2.png\" alt=\"\" class=\"wp-image-270\"\/><\/figure>\n<\/div>\n\n\n<p>Students in <strong>grades 2-4<\/strong> shade grids (or use link cubes) to build area representations of unit fractions 1\/2, 1\/4, 1\/8, and so on, and notice that they all fit in a single square (or square grid of link cubes).<\/p>\n\n\n\n<p>They compare this to walking to the door by repeatedly travelling half the remaining distance. They shade different representations of the fractions (as shown on the right) to create math art.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"alignright size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"191\" height=\"129\" src=\"https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/infinity-3.png\" alt=\"\" class=\"wp-image-271\"\/><\/figure>\n<\/div>\n\n\n<p>Students in <strong>grades 5-9<\/strong> also compare the two fraction patterns on the right and demonstrate that 1\/4 + 1\/16 + 1\/64 + \u2026 = 1\/3 and 1\/2 + 1\/8 + 1\/32 + \u2026 = 2\/3. They also develop an understanding of 0.999\u2026 = 1.<\/p>\n\n\n\n<p>Students in <strong>grade 9<\/strong> also solve a coding puzzle about natural density (which is in Ontario grade 9 mathematics). <\/p>\n\n\n\n<p>In <strong>grades 11-12<\/strong>, students learn about converging series and the role of infinity and limit in Calculus.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Next<\/strong><\/h4>\n\n\n\n<p>Teacher guide &amp; solutions &#8230; <a href=\"https:\/\/learnx.ca\/mt\/infinity-activities\/\">https:\/\/learnx.ca\/mt\/infinity-activities<\/a><\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>placemat placemat Tasks IN THE CLASSROOM Students in grades 2-4 shade grids (or use link cubes) to build area representations of unit fractions 1\/2, 1\/4, 1\/8, and so on, and notice that they all fit in a single square (or square grid of link cubes). They compare this to walking to the door by repeatedly &hellip; <a href=\"https:\/\/learnx.ca\/mt\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;4. Infinity in your Hand&#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":{"footnotes":""},"class_list":["post-259","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/learnx.ca\/mt\/wp-json\/wp\/v2\/pages\/259","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/learnx.ca\/mt\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/learnx.ca\/mt\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/learnx.ca\/mt\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/learnx.ca\/mt\/wp-json\/wp\/v2\/comments?post=259"}],"version-history":[{"count":24,"href":"https:\/\/learnx.ca\/mt\/wp-json\/wp\/v2\/pages\/259\/revisions"}],"predecessor-version":[{"id":889,"href":"https:\/\/learnx.ca\/mt\/wp-json\/wp\/v2\/pages\/259\/revisions\/889"}],"wp:attachment":[{"href":"https:\/\/learnx.ca\/mt\/wp-json\/wp\/v2\/media?parent=259"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}