{"id":862,"date":"2024-07-25T16:15:24","date_gmt":"2024-07-25T16:15:24","guid":{"rendered":"https:\/\/research.ced.ncsu.edu\/ptmt\/?page_id=862"},"modified":"2024-09-30T10:44:01","modified_gmt":"2024-09-30T10:44:01","slug":"teaching-geometry-chapter-5-matrix-representations-and-compositions-of-geometric-transformations","status":"publish","type":"page","link":"https:\/\/research.ced.ncsu.edu\/ptmt\/teaching-geometry\/teaching-geometry-chapter-5-matrix-representations-and-compositions-of-geometric-transformations\/","title":{"rendered":"Teaching Geometry Chapter 5-Matrix Representations and Compositions of Geometric Transformations"},"content":{"rendered":"\n<p class=\"has-text-color has-link-color wp-elements-1 wp-block-paragraph\" style=\"color:#6f7d1c\">Teaching <a href=\"https:\/\/research.ced.ncsu.edu\/ptmt\/teaching-geometry\/\" data-type=\"page\" data-id=\"357\">Geometry<\/a> &gt; Chapter 5<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-group alignwide has-base-2-color has-text-color has-background has-link-color wp-elements-2 has-global-padding is-layout-constrained wp-container-core-group-is-layout-e7ee615e wp-block-group-is-layout-constrained\" style=\"background-color:#7d8c1f;margin-top:0;margin-bottom:0;padding-top:var(--wp--preset--spacing--10);padding-right:var(--wp--preset--spacing--10);padding-bottom:var(--wp--preset--spacing--10);padding-left:var(--wp--preset--spacing--10)\">\n<div class=\"wp-block-group alignwide has-background has-global-padding is-layout-constrained wp-container-core-group-is-layout-7bc61772 wp-block-group-is-layout-constrained\" style=\"background-color:#7d8c1f;padding-right:var(--wp--preset--spacing--10);padding-left:var(--wp--preset--spacing--10)\">\n<div class=\"wp-block-group alignwide is-vertical is-content-justification-center is-layout-flex wp-container-core-group-is-layout-bc18b00a wp-block-group-is-layout-flex\">\n<div class=\"wp-block-columns has-base-2-color has-text-color has-background has-link-color wp-elements-3 is-layout-flex wp-container-core-columns-is-layout-17e9b11e wp-block-columns-is-layout-flex\" style=\"background-color:#7d8c1f;padding-top:0;padding-right:var(--wp--preset--spacing--10);padding-bottom:0;padding-left:var(--wp--preset--spacing--10)\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:15%\"><figure style=\"padding-top:0;padding-bottom:0;padding-left:var(--wp--preset--spacing--10);padding-right:var(--wp--preset--spacing--10)\" class=\"alignleft wp-block-post-featured-image\"><img loading=\"lazy\" decoding=\"async\" width=\"1332\" height=\"1320\" src=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/05\/geo_page_logo.png\" class=\"attachment-post-thumbnail size-post-thumbnail wp-post-image\" alt=\"\" style=\"height:150px;object-fit:contain;\" srcset=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/05\/geo_page_logo.png 1332w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/05\/geo_page_logo-300x297.png 300w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/05\/geo_page_logo-1024x1015.png 1024w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/05\/geo_page_logo-150x150.png 150w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/05\/geo_page_logo-768x761.png 768w\" sizes=\"auto, (max-width: 1332px) 100vw, 1332px\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-top is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:85%\"><h2 style=\"background-color:#7d8c1f;font-size:clamp(1.743rem, 1.743rem + ((1vw - 0.2rem) * 2.095), 3rem);font-style:normal;font-weight:800\" class=\"has-link-color wp-elements-4 wp-block-post-title has-text-color has-base-2-color has-background\">Teaching Geometry Chapter 5-Matrix Representations and Compositions of Geometric Transformations<\/h2><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\">Geometric transformations have long been an important part of school mathematics curricula. They are appealing to students because of their applicability to the world around us and provide opportunities to employ different mathematical tools to engage in reasoning and sense-making activities. Geometric descriptions, algebraic equations, and matrices are all different representations one can use to think about geometric transformations. In this chapter, teachers will focus on algebraic and matrix representations and consider how they can be used to describe geometric transformations in the plane. Teachers will also examine compositions of geometric transformations and determine how these compositions are related to the geometric transformations we focused on in Chapter 4.<\/p>\n<\/div>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center\" style=\"font-size:clamp(1.743rem, 1.743rem + ((1vw - 0.2rem) * 2.095), 3rem);\"><strong>Class Materials<\/strong><\/h3>\n\n\n\n<div class=\"wp-block-group alignwide has-background has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\" style=\"background-color:#7d8c1f\">\n<div style=\"height:5px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-columns alignwide is-layout-flex wp-container-core-columns-is-layout-180f4183 wp-block-columns-is-layout-flex\" style=\"padding-top:var(--wp--preset--spacing--10);padding-bottom:var(--wp--preset--spacing--10)\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-media-text is-stacked-on-mobile\" style=\"grid-template-columns:22% auto\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"256\" src=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white.png\" alt=\"\" class=\"wp-image-634 size-full\" srcset=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white.png 256w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white-150x150.png 150w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<p class=\"has-base-2-color has-text-color has-link-color wp-elements-5 wp-block-paragraph\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/drive.google.com\/file\/d\/1q7s_VwgE2KbIjIenZ0GN0eUKCXKfBXiv\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Chapter Document<\/strong><\/a><\/p>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-media-text is-stacked-on-mobile\" style=\"grid-template-columns:22% auto\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"256\" src=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/015-camera-1.png\" alt=\"\" class=\"wp-image-636 size-full\" srcset=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/015-camera-1.png 256w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/015-camera-1-150x150.png 150w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<p class=\"has-base-2-color has-text-color has-link-color wp-elements-6 wp-block-paragraph\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/drive.google.com\/file\/d\/1vxLk5hM7iUn7880Wur4N34JNc6830SqF\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Video Transcripts<\/strong><\/a><\/p>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-media-text is-stacked-on-mobile\" style=\"grid-template-columns:22% auto\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"256\" src=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/014-download-2.png\" alt=\"\" class=\"wp-image-638 size-full\" srcset=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/014-download-2.png 256w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/014-download-2-150x150.png 150w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<p class=\"has-base-2-color has-text-color has-link-color wp-elements-7 wp-block-paragraph\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/drive.google.com\/file\/d\/1nPjc5B9kpjS361WIzX1tabgvtxlVyS3E\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Download Tech Files<\/strong><\/a><\/p>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center\" style=\"font-size:clamp(1.743rem, 1.743rem + ((1vw - 0.2rem) * 2.095), 3rem);\"><strong>Instructor Materials<\/strong><\/h3>\n\n\n\n<div class=\"wp-block-group alignwide has-background has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\" style=\"background-color:#7d8c1f\">\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-columns alignwide is-layout-flex wp-container-core-columns-is-layout-180f4183 wp-block-columns-is-layout-flex\" style=\"padding-top:var(--wp--preset--spacing--10);padding-bottom:var(--wp--preset--spacing--10)\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-media-text is-stacked-on-mobile\" style=\"grid-template-columns:22% auto\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"256\" src=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white.png\" alt=\"\" class=\"wp-image-634 size-full\" srcset=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white.png 256w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white-150x150.png 150w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<p class=\"has-base-2-color has-text-color has-link-color wp-elements-8 wp-block-paragraph\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/drive.google.com\/file\/d\/1-mMy5KmyVESc9KwtmlCYfkxu1pChgY6G\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Teaching Tips<\/strong><\/a><\/p>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-media-text is-stacked-on-mobile\" style=\"grid-template-columns:22% auto\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"256\" src=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white.png\" alt=\"\" class=\"wp-image-634 size-full\" srcset=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white.png 256w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white-150x150.png 150w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<p class=\"has-base-2-color has-text-color has-link-color wp-elements-9 wp-block-paragraph\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/drive.google.com\/file\/d\/1DR_KPWMHbT4WUVL5GLhXpk2nMucrBDQL\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Suggested Readings<\/strong><\/a><\/p>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-media-text is-stacked-on-mobile\" style=\"grid-template-columns:22% auto\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"256\" src=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white.png\" alt=\"\" class=\"wp-image-634 size-full\" srcset=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white.png 256w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white-150x150.png 150w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<p class=\"has-base-2-color has-text-color has-link-color wp-elements-10 wp-block-paragraph\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/drive.google.com\/file\/d\/1vhRnCskvZmCGKUu_hxNcA0Flec26MLpG\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Sample Solutions<\/strong><\/a><\/p>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Teaching Geometry &gt; Chapter 5 Geometric transformations have long been an important part of school mathematics curricula. They are appealing to students because of their applicability to the world around us and provide opportunities to employ different mathematical tools to engage in reasoning and sense-making activities. Geometric descriptions, algebraic equations, and matrices are all different [&hellip;]<\/p>\n","protected":false},"author":66,"featured_media":231,"parent":357,"menu_order":5,"comment_status":"closed","ping_status":"closed","template":"test-blank-page","meta":{"_acf_changed":false,"ncst_custom_author":"","ncst_show_custom_author":false,"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-862","page","type-page","status-publish","has-post-thumbnail","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/862","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/users\/66"}],"replies":[{"embeddable":true,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/comments?post=862"}],"version-history":[{"count":6,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/862\/revisions"}],"predecessor-version":[{"id":1824,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/862\/revisions\/1824"}],"up":[{"embeddable":true,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/357"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/media\/231"}],"wp:attachment":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/media?parent=862"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}