{"id":132,"date":"2024-08-22T13:31:08","date_gmt":"2024-08-22T13:31:08","guid":{"rendered":"https:\/\/learnx.ca\/mt\/?page_id=132"},"modified":"2025-08-18T08:00:34","modified_gmt":"2025-08-18T08:00:34","slug":"activities-growing-patterns","status":"publish","type":"page","link":"https:\/\/learnx.ca\/mt\/activities-growing-patterns\/","title":{"rendered":"PLACEMAT TASKS"},"content":{"rendered":"\n<p>[<a href=\"#s\">Solutions<\/a>&nbsp;are shown after the activities]<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">TASK 1: What do you See?<\/h4>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"473\" height=\"395\" src=\"https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a1.png\" alt=\"\" class=\"wp-image-152\" srcset=\"https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a1.png 473w, https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a1-300x251.png 300w\" sizes=\"auto, (max-width: 473px) 85vw, 473px\" \/><\/figure>\n\n\n\n<p><strong>EXTENSIONS<\/strong><\/p>\n\n\n\n<p><strong>Build a new growing pattern<\/strong><\/p>\n\n\n\n<p>Ask students to build their own growing pattern and complete a table of values.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"321\" height=\"200\" src=\"https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a6.png\" alt=\"\" class=\"wp-image-155\" srcset=\"https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a6.png 321w, https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a6-300x187.png 300w\" sizes=\"auto, (max-width: 321px) 85vw, 321px\" \/><\/figure>\n\n\n\n<p><strong>Algebraic expressions<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"alignright size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"249\" height=\"97\" src=\"https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a7.png\" alt=\"\" class=\"wp-image-156\"\/><\/figure>\n<\/div>\n\n\n<p>The train patterns below represent linear equations students may study in grades 8-9:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>y = 3x + 3<\/li>\n\n\n\n<li>y = x + 1<\/li>\n\n\n\n<li>y = 2x + 1<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">TASK 2: Complete the graph<\/h4>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"374\" height=\"328\" src=\"https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a4.png\" alt=\"\" class=\"wp-image-153\" srcset=\"https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a4.png 374w, https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a4-300x263.png 300w\" sizes=\"auto, (max-width: 374px) 85vw, 374px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">TASK 3: What is different?<\/h4>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"426\" height=\"311\" src=\"https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a8.png\" alt=\"\" class=\"wp-image-158\" srcset=\"https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a8.png 426w, https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a8-300x219.png 300w\" sizes=\"auto, (max-width: 426px) 85vw, 426px\" \/><\/figure>\n\n\n\n<p><strong>EXTENSION<\/strong><\/p>\n\n\n\n<p>Model and then ask students to investigate the simulation at <a href=\"https:\/\/imaginethis.ca\/mathncode\/sims-growpatt.html\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/imaginethis.ca\/mathncode\/sims-growpatt.html<\/a><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"237\" height=\"165\" src=\"https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a10.png\" alt=\"\" class=\"wp-image-159\" style=\"width:310px;height:auto\"\/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">TASK 4: How does the pattern grow?<\/h4>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"483\" height=\"329\" src=\"https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a11.png\" alt=\"\" class=\"wp-image-160\" srcset=\"https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a11.png 483w, https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a11-300x204.png 300w\" sizes=\"auto, (max-width: 483px) 85vw, 483px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading has-dark-gray-color has-text-color has-link-color wp-elements-fd657f999b5c075dfd639e73e4ea691e\" id=\"s\">SOLUTIONS<\/h1>\n\n\n\n<h4 class=\"wp-block-heading\">TASK 1: What do you see?<\/h4>\n\n\n\n<p>What students might see:<\/p>\n\n\n\n<p><strong>1.&nbsp; Growing patterns on train cars<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"alignright size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"325\" height=\"126\" src=\"https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a2.png\" alt=\"\" class=\"wp-image-149\" srcset=\"https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a2.png 325w, https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a2-300x116.png 300w\" sizes=\"auto, (max-width: 325px) 85vw, 325px\" \/><\/figure>\n<\/div>\n\n\n<p>Students may notice the growing patterns of blue and pink blocks on train cars.<\/p>\n\n\n\n<p>Give students link cubes, or chart paper and dabbers. Ask students to reproduce the patterns.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>How do the patterns grow?<\/li>\n\n\n\n<li>What changes? What stays the same?<\/li>\n\n\n\n<li>What would be on the 5<sup>th<\/sup> train car?<\/li>\n\n\n\n<li>On the 10<sup>th<\/sup>? On the 100<sup>th<\/sup>?<\/li>\n<\/ul>\n\n\n\n<p><strong>2.&nbsp; Bar graphs<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"alignright size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"290\" height=\"123\" src=\"https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a3.png\" alt=\"\" class=\"wp-image-150\"\/><\/figure>\n<\/div>\n\n\n<p>Students may notice the bar graphs made of blue and pink pebbles.<\/p>\n\n\n\n<p>Give students link cubes, or chart paper and dabbers. Ask students to reproduce the bar graphs. What creates growth? The blue or pink pebbles? (Students will revisit this in Activity 3.)<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">TASK 2: Complete the graph<\/h4>\n\n\n\n<p>Young students love to work with large numbers. Don\u2019t hesitate to ask them how may blocks might be needed to build the 1000<sup>th<\/sup> stage.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"374\" height=\"328\" src=\"https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a4-1.png\" alt=\"\" class=\"wp-image-154\" srcset=\"https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a4-1.png 374w, https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a4-1-300x263.png 300w\" sizes=\"auto, (max-width: 374px) 85vw, 374px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">TASK 3: What is different?<\/h4>\n\n\n\n<p>Both bar graphs represent the pattern shown below.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"340\" height=\"83\" src=\"https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a9.png\" alt=\"\" class=\"wp-image-161\" srcset=\"https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a9.png 340w, https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a9-300x73.png 300w\" sizes=\"auto, (max-width: 340px) 85vw, 340px\" \/><\/figure>\n\n\n\n<p>The pink pebbles are on top of the blue pebbles in the first bar graph, and vice versa in the second bar graph.<\/p>\n\n\n\n<p>This helps students see that it is the blue pebbles (whose number varies or increases) that make the pattern grow at each stage.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">TASK 4: How does the pattern grow?<\/h4>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"alignright size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"236\" height=\"218\" src=\"https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a12.png\" alt=\"\" class=\"wp-image-162\"\/><\/figure>\n<\/div>\n\n\n<p>This pattern represents the growth of bacteria, which grow by dividing themselves in two.<\/p>\n\n\n\n<p>So, 2 bacteria lead to 4, which lead to 8, which lead to 16.<\/p>\n\n\n\n<p>This doubling pattern, shown in green on the right, is called exponential growth. Its algebraic expression is 2<sup>x<\/sup>, where x is the stage number.<\/p>\n\n\n\n<p>Dr. Lindi Wahl, applied mathematician at Western University, builds and discusses this growing pattern in the 5<sup>th<\/sup> video, <em>How Bacteria Grow<\/em>, at <a href=\"https:\/\/imaginethis.ca\/lindi-wahl\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/imaginethis.ca\/lindi-wahl<\/a>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"273\" height=\"123\" src=\"https:\/\/learnx.ca\/mt\/wp-content\/uploads\/2024\/08\/trains-a13.png\" alt=\"\" class=\"wp-image-163\"\/><\/figure>\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>Coding puzzles &#8230; <a href=\"https:\/\/learnx.ca\/mt\/coding-growing-patterns\/\">https:\/\/learnx.ca\/mt\/coding-growing-patterns<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>[Solutions&nbsp;are shown after the activities] TASK 1: What do you See? EXTENSIONS Build a new growing pattern Ask students to build their own growing pattern and complete a table of values. Algebraic expressions The train patterns below represent linear equations students may study in grades 8-9: TASK 2: Complete the graph TASK 3: What is &hellip; <a href=\"https:\/\/learnx.ca\/mt\/activities-growing-patterns\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;PLACEMAT TASKS&#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-132","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/learnx.ca\/mt\/wp-json\/wp\/v2\/pages\/132","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=132"}],"version-history":[{"count":20,"href":"https:\/\/learnx.ca\/mt\/wp-json\/wp\/v2\/pages\/132\/revisions"}],"predecessor-version":[{"id":832,"href":"https:\/\/learnx.ca\/mt\/wp-json\/wp\/v2\/pages\/132\/revisions\/832"}],"wp:attachment":[{"href":"https:\/\/learnx.ca\/mt\/wp-json\/wp\/v2\/media?parent=132"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}