{"id":822,"date":"2024-07-25T12:42:58","date_gmt":"2024-07-25T12:42:58","guid":{"rendered":"https:\/\/research.ced.ncsu.edu\/ptmt\/?page_id=822"},"modified":"2024-09-30T15:05:37","modified_gmt":"2024-09-30T15:05:37","slug":"teaching-algebra-chapter-4-equivalence-and-equality","status":"publish","type":"page","link":"https:\/\/research.ced.ncsu.edu\/ptmt\/teaching-algebra\/teaching-algebra-chapter-4-equivalence-and-equality\/","title":{"rendered":"Teaching Algebra Chapter 4-Equivalence and Equality"},"content":{"rendered":"\n<p class=\"has-text-color has-link-color wp-elements-e22e75a0616e4ab4730f778665306509\" style=\"color:#d14905\"><a href=\"https:\/\/research.ced.ncsu.edu\/ptmt\/teaching-algebra\/\" data-type=\"page\" data-id=\"71\">Teaching Algebra<\/a> &gt; Chapter 4<\/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-15cc4fbce9807760812dd463ea111746 has-global-padding is-layout-constrained wp-container-core-group-is-layout-9daa8ca1 wp-block-group-is-layout-constrained\" style=\"background-color:#d14905;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-1be0671b wp-block-group-is-layout-constrained\" style=\"background-color:#d14905;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-ce155fab 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-5aade4b5c3938c0cdb5f5ba6bc0dbd7d is-layout-flex wp-container-core-columns-is-layout-28747e1f wp-block-columns-is-layout-flex\" style=\"background-color:#d14905;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=\"height:150px; 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=\"250\" height=\"252\" src=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/alg_page_logo_250x252.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\/07\/alg_page_logo_250x252.png 250w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/alg_page_logo_250x252-150x150.png 150w\" sizes=\"auto, (max-width: 250px) 100vw, 250px\" \/><\/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:#d14905; 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-fbed58c1dcfb124481494af6efad93d2 wp-block-post-title has-text-color has-base-2-color has-background\">Teaching Algebra Chapter 4-Equivalence and Equality<\/h2><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<p style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\">Equality and the equal sign (i.e., \u2018=\u2019) are introduced to students during the early elementary years, and as a result, student understanding of the symbol is often taken for granted. However, understanding equality and equivalence symbolically, graphically, and numerically is beneficial for success in algebra at all levels. In this chapter we will use GeoGebra and existing applets to explore properties of equality, equivalence, solutions to equations, and equivalent forms of common equations.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-base-2-color has-alpha-channel-opacity has-base-2-background-color has-background is-style-wide\" \/>\n\n\n\n<p style=\"padding-right:0;padding-left:0;font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><img loading=\"lazy\" decoding=\"async\" width=\"56\" height=\"56\" src=\"https:\/\/lh7-us.googleusercontent.com\/docsz\/AD_4nXcjAd2LaOquLZl6f1QVpgTFIR0s-x34bYMeOj5KF22AC9imcETtmdweOx7T0KKEbvi6hPoKHHeOmirNbUmwGSZFMsa1rYA1i76c46HlNoe-0_QhuB83R-Btv18oQLTRuFQVQvdyy67SaTOI24g1orW2j8E_?key=_-Ah_2wP0wYww8pv4LkjOg\" alt=\"ESP Logo\"> This chapter could be used alongside a Module within the Examining Students&#8217; Practices (ESP) in Algebra and Function:<\/p>\n\n\n\n<p style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/research.ced.ncsu.edu\/ptmt\/examining-students-practices-in-algebra-and-function\/esp-module-2-algebraic-equivalence\/\" data-type=\"page\" data-id=\"760\"><strong>Module 2:<\/strong><\/a>\u00a0Algebraic Equivalence<\/p>\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>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:#d14905\">\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-28b55a6e 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:15% 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-3908b01e22290b3a8af42c4ef042dbd6\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/drive.google.com\/file\/d\/1mH6y76jA4Nj_KNNMOw8iJSXwJdhdezMB\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Chapter Document<\/strong><\/a><\/p>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:21px\" 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:#d14905\">\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-28b55a6e 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-845e05272a8124895985addcfb4233c2\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/drive.google.com\/file\/d\/1QTywf44QtQ68I6o8AEc70StWn_9Fm112\/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-c219c7931dc198988ef5d516d2793411\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/drive.google.com\/file\/d\/1mSxAP6affH7V28UOreEDlzqjbxR2uMtc\/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-98a02905057684a1a8550a0bccf819da\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/drive.google.com\/file\/d\/1ICESp6saWdoszjKBirMCwhxjzN9M7MzG\/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 Algebra &gt; Chapter 4 Equality and the equal sign (i.e., \u2018=\u2019) are introduced to students during the early elementary years, and as a result, student understanding of the symbol is often taken for granted. However, understanding equality and equivalence symbolically, graphically, and numerically is beneficial for success in algebra at all levels. In this [&hellip;]<\/p>\n","protected":false},"author":66,"featured_media":651,"parent":71,"menu_order":4,"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-822","page","type-page","status-publish","has-post-thumbnail","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/822","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=822"}],"version-history":[{"count":13,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/822\/revisions"}],"predecessor-version":[{"id":1876,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/822\/revisions\/1876"}],"up":[{"embeddable":true,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/71"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/media\/651"}],"wp:attachment":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/media?parent=822"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}