{"id":228,"date":"2022-04-13T08:46:25","date_gmt":"2022-04-13T08:46:25","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=228"},"modified":"2025-04-08T11:49:42","modified_gmt":"2025-04-08T11:49:42","slug":"n-1-model-and-solve-equations-using-algebra-tiles","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/n-1-model-and-solve-equations-using-algebra-tiles\/","title":{"rendered":"N.1 Model and solve equations using algebra tiles"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Model and solve equations using algebra tiles<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-869a5c0b6b78055316c8d0186252dcbd\" style=\"color:#74008b\"><strong>key notes :<\/strong><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-332c59594839aa9fc0f8cb38777fe2b4\" style=\"color:#000060\"><strong>What Are Algebra Tiles?<\/strong><\/h4>\n\n\n\n<p class=\"has-large-font-size\"><strong>Algebra tiles<\/strong> are <strong>manipulatives<\/strong> used to visually represent algebraic expressions and equations.<\/p>\n\n\n\n<p class=\"has-large-font-size\">Types of tiles:<\/p>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li><strong>Unit tile (small square)<\/strong> = 1<\/li>\n\n\n\n<li><strong>x-tile (rectangle)<\/strong> = x<\/li>\n\n\n\n<li><strong>x\u00b2-tile (large square)<\/strong> = x\u00b2<\/li>\n\n\n\n<li><strong>Negative tiles<\/strong> are usually <strong>red<\/strong> or a different color.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-6ebdaaaa7bd4ae9d9712b5f68d02e3e2\" style=\"color:#000060\"><strong>Purpose of Using Algebra Tiles<\/strong><\/h4>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>Helps students <strong>visualize and understand<\/strong> abstract algebraic concepts.<\/li>\n\n\n\n<li>Makes it easier to model <strong>equations<\/strong>, <strong>simplify expressions<\/strong>, and <strong>solve equations<\/strong> step by step.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-fb2e7f3f6963ef23e17024af281b7e6c\" style=\"color:#000060\"><strong>Modeling Expressions<\/strong><\/h4>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>Represent algebraic expressions like <strong>x + 3<\/strong>, <strong>2x &#8211; 1<\/strong>, using a combination of positive and negative tiles.<\/li>\n\n\n\n<li>Positive x \u2192 green rectangle, Negative x \u2192 red rectangle.<\/li>\n\n\n\n<li>Positive 1 \u2192 green square, Negative 1 \u2192 red square.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-0fcf08b61e01d19785ce9d8b810346da\" style=\"color:#000060\"><strong>Setting Up the Equation<\/strong><\/h4>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>Use a <strong>mat<\/strong> or draw a <strong>balance scale<\/strong> to model both sides of an equation (e.g., <strong>x + 3 = 2x &#8211; 1<\/strong>).<\/li>\n\n\n\n<li>Place corresponding tiles on each side of the equal sign to represent each expression.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-c6955c2966000271b51bea0cdfe3293b\" style=\"color:#000060\"><strong>Solving the Equation<\/strong><\/h4>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li><strong>Step 1:<\/strong> Use <strong>zero pairs<\/strong> to eliminate tiles on both sides (e.g., +x and -x cancel each other).<\/li>\n\n\n\n<li><strong>Step 2:<\/strong> Isolate the <strong>variable tile<\/strong> on one side of the equation.<\/li>\n\n\n\n<li><strong>Step 3:<\/strong> Balance the equation by adding\/removing tiles <strong>equally<\/strong> on both sides.<\/li>\n\n\n\n<li><strong>Step 4:<\/strong> Count the number of unit tiles to find the value of <strong>x<\/strong>.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-5b8d6bc6538d78f23b472b8d9c7c55cc\" style=\"color:#000060\"><strong>Zero Pairs<\/strong><\/h4>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>A <strong>positive tile<\/strong> and a <strong>negative tile<\/strong> together form a <strong>zero pair<\/strong> (e.g., +1 and -1 = 0).<\/li>\n\n\n\n<li>Used to <strong>eliminate<\/strong> tiles and keep the equation <strong>balanced<\/strong>.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-e6fad15c1b8bde9fbb27558be28db999\" style=\"color:#000060\"><strong>Check Your Solution<\/strong><\/h4>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>After finding the value of <strong>x<\/strong>, substitute it back into the original equation to verify.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-fdb730c2e970ec4766f1c303e0aa9662\" style=\"color:#000060\"><strong>Advantages for Students<\/strong><\/h4>\n\n\n\n<ul class=\"has-large-font-size wp-block-list\">\n<li>Builds <strong>conceptual understanding<\/strong> before abstract methods.<\/li>\n\n\n\n<li>Enhances <strong>problem-solving<\/strong> and <strong>logical reasoning<\/strong> skills.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-9b08f5118a4cf7a27c66c68145f9dd8f\" style=\"color:#000060\"><strong>\u270f\ufe0f Example:<\/strong><\/h3>\n\n\n\n<p class=\"has-large-font-size\">Solve <strong>x + 2 = 3<\/strong> using algebra tiles:<\/p>\n\n\n\n<ol class=\"has-large-font-size wp-block-list\">\n<li>Left side: 1 x-tile + 2 unit tiles.<\/li>\n\n\n\n<li>Right side: 3 unit tiles.<\/li>\n\n\n\n<li>Remove 2 unit tiles from both sides.<\/li>\n\n\n\n<li>Left: 1 x-tile, Right: 1 unit tile \u2192 So, <strong>x = 1<\/strong>.<\/li>\n<\/ol>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#e79f9f\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>Which&nbsp;equation does this set of algebra tiles&nbsp;represent?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"603\" height=\"207\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-6.png\" alt=\"\" class=\"wp-image-12014\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-6.png 603w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-6-300x103.png 300w\" sizes=\"auto, (max-width: 603px) 100vw, 603px\" \/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>8x = 8<\/li>\n\n\n\n<li>7x = 7<\/li>\n\n\n\n<li>2x = 10<\/li>\n\n\n\n<li>5x = 10<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Look&nbsp;at the tiles on the left side of the&nbsp;set.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"292\" height=\"178\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T125300.499.png\" alt=\"\" class=\"wp-image-12020\" style=\"aspect-ratio:1.6404494382022472;width:305px;height:auto\"\/><\/figure><\/div>\n\n\n<p>The left side has 5 (x) tiles. So, the left side of the equation should be 5x.<\/p>\n\n\n\n<p>Now&nbsp;look at the tiles on the right side of the&nbsp;set.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"206\" height=\"135\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T125319.896.png\" alt=\"\" class=\"wp-image-12021\" style=\"aspect-ratio:1.525925925925926;width:285px;height:auto\"\/><\/figure><\/div>\n\n\n<p>The right side has 10 (1) tiles. So, the right side of the equation should be 10.<\/p>\n\n\n\n<p>This set of algebra tiles represents the equation 5x=10.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#b7ecb7\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>Which&nbsp;equation does this set of algebra tiles&nbsp;represent?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"496\" height=\"218\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-10.png\" alt=\"\" class=\"wp-image-12022\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-10.png 496w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-10-300x132.png 300w\" sizes=\"auto, (max-width: 496px) 100vw, 496px\" \/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>&#8211; X &#8211; 4 = 8<\/li>\n\n\n\n<li>&#8211; X &#8211; 4 = -9<\/li>\n\n\n\n<li>&#8211; X &#8211; 4 = 4<\/li>\n\n\n\n<li>&#8211; X &#8211; 4 = 17<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Look&nbsp;at the tiles on the left side of the&nbsp;set.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"199\" height=\"173\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T125801.619.png\" alt=\"\" class=\"wp-image-12023\"\/><\/figure><\/div>\n\n\n<p>The left side has 1(-x ) tile and 4 (-1) tiles. So, the left side of the equation should be \u2013x\u20134.<\/p>\n\n\n\n<p>Now&nbsp;look at the tiles on the right side of the&nbsp;set.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"192\" height=\"156\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T125952.761.png\" alt=\"\" class=\"wp-image-12025\" style=\"aspect-ratio:1.2307692307692308;width:219px;height:auto\"\/><\/figure><\/div>\n\n\n<p>The right side has 9(-1) tiles. So, the right side of the equation should be\u20139.<\/p>\n\n\n\n<p>This set of algebra tiles represents the equation \u2013x\u20134=\u20139.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#afd0ed\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>Which&nbsp;equation does this set of algebra tiles&nbsp;represent?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"738\" height=\"203\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-11.png\" alt=\"\" class=\"wp-image-12031\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-11.png 738w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-11-300x83.png 300w\" sizes=\"auto, (max-width: 738px) 100vw, 738px\" \/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>&#8211; X &#8211; 4 = 17<\/li>\n\n\n\n<li>&#8211; X &#8211; 7 = 17<\/li>\n\n\n\n<li>&#8211; X + 9 = 17<\/li>\n\n\n\n<li>&#8211; X &#8211; 5 = 17<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Look&nbsp;at the tiles on the left side of the&nbsp;set.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"241\" height=\"170\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T131102.441.png\" alt=\"\" class=\"wp-image-12035\"\/><\/figure><\/div>\n\n\n<p>The left side has 1 (-X)  tile and 9  (1)  tiles. So, the left side of the equation should be  \u2013 X+9.<\/p>\n\n\n\n<p>Now&nbsp;look at the tiles on the right side of the&nbsp;set.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"343\" height=\"175\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T131233.297.png\" alt=\"\" class=\"wp-image-12036\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T131233.297.png 343w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T131233.297-300x153.png 300w\" sizes=\"auto, (max-width: 343px) 100vw, 343px\" \/><\/figure><\/div>\n\n\n<p>The right side has 17(1) tiles. So, the right side of the equation should be 17.<\/p>\n\n\n\n<p>This set of algebra tiles represents the equation \u2013 X + 9 = 17.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let`s practice!<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/90018\/491\/973\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-88.png\" alt=\"\" class=\"wp-image-7956\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-88.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-88-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-88-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/90018\/322\/891\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-97.png\" alt=\"\" class=\"wp-image-7957\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-97.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-97-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-97-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Model and solve equations using algebra tiles key notes : What Are Algebra Tiles? Algebra tiles are manipulatives used to visually represent algebraic expressions and equations. Types of tiles: Purpose of Using Algebra Tiles Modeling Expressions Setting Up the Equation Solving the Equation Zero Pairs Check Your Solution Advantages for Students \u270f\ufe0f Example: Solve x<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/n-1-model-and-solve-equations-using-algebra-tiles\/\">Continue reading <span class=\"screen-reader-text\">&#8220;N.1 Model and solve equations using algebra tiles&#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":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-228","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/228","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=228"}],"version-history":[{"count":17,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/228\/revisions"}],"predecessor-version":[{"id":16682,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/228\/revisions\/16682"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=228"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}