{"id":501,"date":"2022-04-13T05:22:33","date_gmt":"2022-04-13T05:22:33","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=501"},"modified":"2025-02-23T06:53:39","modified_gmt":"2025-02-23T06:53:39","slug":"y-6-factorise-quadratics-using-algebra-tiles","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/y-6-factorise-quadratics-using-algebra-tiles\/","title":{"rendered":"Y.6 Factorise quadratics 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>Factorise quadratics using algebra tiles<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-a7babd01df25c034f9938b577dbd6ba0\" style=\"color:#74008b;text-transform:capitalize\">key notes :<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-e55c2de215b7f6488d1dafb4d0c323c9\" style=\"color:#000060\"><strong>Understanding Algebra Tiles<\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size\">Algebra tiles are manipulatives that represent algebraic expressions visually.<\/p>\n\n\n\n<p class=\"has-large-font-size\">Different tiles represent different terms:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Large square:<\/strong> x<sup>2<\/sup><\/li>\n\n\n\n<li><strong>Rectangle:<\/strong> x<\/li>\n\n\n\n<li><strong>Small square:<\/strong> Constant (1)<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-5cb22dbda880b26cf3053c3d93609768\" style=\"color:#000060\"><strong>Structure of a Quadratic Expression<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>A quadratic expression is in the form <strong>ax<sup>2<\/sup> + bx + c<\/strong><\/li>\n\n\n\n<li>Factorising means rewriting it as a product of two binomials: <strong>(x + m)(x + n)<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-d9e58727aad0514629a01efa165ce1b7\" style=\"color:#000060\"><strong>Arranging Tiles to Form a Rectangle<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Place the <strong>x<sup>2<\/sup> tile(s)<\/strong> in one section.<\/li>\n\n\n\n<li>Arrange <strong>x tiles<\/strong> to represent the middle term.<\/li>\n\n\n\n<li>Place <strong>unit tiles<\/strong> for the constant term.<\/li>\n\n\n\n<li>The goal is to form a complete rectangle.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-1a6e68d280a1846a2a94419b5cbe04d6\" style=\"color:#000060\"><strong>Finding the Factors<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Identify two numbers that multiply to <strong>c<\/strong> and add to <strong>b<\/strong>.<\/li>\n\n\n\n<li>These numbers determine how the tiles are grouped into rows and columns.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-672e0c7321588103e117329a80077d73\" style=\"color:#000060\"><strong>Writing the Factored Form<\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size\">The binomial factors correspond to the dimensions of the rectangle.<\/p>\n\n\n\n<p class=\"has-large-font-size\">Example: If the factors are <strong>(x + 3)(x + 2)<\/strong>, this means:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>The length of the rectangle = x + 3<\/li>\n\n\n\n<li>The width of the rectangle = x + 2<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-f7c4a402599a68faf4300120638d86c3\" style=\"color:#000060\"><strong>Checking the Factorisation<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Expand the binomials to verify:<br>(x + m)(x + n) = x<sup>2<\/sup> + (m + n) x + mn.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-9fb9620f7199f8f2abf371e7dcf876f3\" style=\"color:#000060\"><strong>Special Cases<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Perfect square trinomials<\/strong>: Tiles form a square (e.g., x<sup>2<\/sup> + 6x + 9 = (x + 3)(x + 3).<\/li>\n\n\n\n<li><strong>Difference of squares<\/strong>: No middle term, factors as (x + a)(x \u2212 a).<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-4fba4ed7fa3dfb5375e0236c182f015d\" style=\"color:#000060\"><strong>Benefits of Using Algebra Tiles<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Provides a visual and hands-on approach to learning.<\/li>\n\n\n\n<li>Helps students understand the connection between area and factorisation.<\/li>\n\n\n\n<li>Makes abstract algebra more concrete and intuitive.<\/li>\n<\/ul>\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-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background\" style=\"background-color:#e9f2a9\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-dc6e2b0a221097b3f0e1e94b3a5bedb7\" style=\"color:#b00012\">\ud83e\udd4e <strong>Which&nbsp;area model represents the factorisation&nbsp;6x<sup>2<\/sup>+7x+2=(3x+2)(2x+1)?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-6-1.png\" alt=\"\" class=\"wp-image-6484\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-6-1.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-6-1-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-6-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"200\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-500-\u00d7-200px-9.png\" alt=\"\" class=\"wp-image-6485\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-500-\u00d7-200px-9.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-500-\u00d7-200px-9-300x120.png 300w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-7-1.png\" alt=\"\" class=\"wp-image-6486\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-7-1.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-7-1-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-7-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-8-1.png\" alt=\"\" class=\"wp-image-6487\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-8-1.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-8-1-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-8-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<p>This&nbsp;area model represents the factorisation&nbsp;6x<sup>2<\/sup>+7x+2=(3x+2)(2x+1).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"200\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___200px___1_-removebg-preview-3.png\" alt=\"\" class=\"wp-image-6488\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___200px___1_-removebg-preview-3.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___200px___1_-removebg-preview-3-300x120.png 300w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>The&nbsp;left side of the equation represents the total area written as the sum of all the tiles. There are&nbsp;6&nbsp;<em>x<\/em>2&nbsp;tiles,&nbsp;7&nbsp;<em>x<\/em>&nbsp;tiles, and&nbsp;2&nbsp;1&nbsp;tiles, so the sum is&nbsp;6x<sup>2<\/sup>+7x+2.<\/p>\n\n\n\n<p>The&nbsp;right side of the equation represents the total area written as base times height. The base is made up of&nbsp;3&nbsp;<em>x<\/em>&nbsp;tiles and&nbsp;2&nbsp;1&nbsp;tiles, so it is&nbsp;(3x+2).&nbsp;The height is made up of&nbsp;2&nbsp;<em>x<\/em>&nbsp;tiles and&nbsp;1&nbsp;1&nbsp;tile, so it is&nbsp;(2x+1).&nbsp;The base times the height is&nbsp;(3x+2)(2x+1).<\/p>\n\n\n\n<p>The&nbsp;other area models represent factorisations of different&nbsp;polynomials.<\/p>\n\n\n\n<p>This&nbsp;area model shows&nbsp;6x<sup>2<\/sup>+10x+4=(3x+2)(2x+2).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__6_-removebg-preview-1.png\" alt=\"\" class=\"wp-image-6489\" style=\"width:379px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__6_-removebg-preview-1.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__6_-removebg-preview-1-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__6_-removebg-preview-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>This&nbsp;area model shows&nbsp;3x<sup>2<\/sup>+5x+2=(3x+2)(x+1).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"200\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-500-\u00d7-200px-10.png\" alt=\"\" class=\"wp-image-6490\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-500-\u00d7-200px-10.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-500-\u00d7-200px-10-300x120.png 300w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>This&nbsp;area model shows&nbsp;9x<sup>2<\/sup>+12x+4=(3x+2)(3x+2).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__7_-removebg-preview.png\" alt=\"\" class=\"wp-image-6491\" style=\"width:367px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__7_-removebg-preview.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__7_-removebg-preview-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__7_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#c2f9ae\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-2743ab2a15ab294a9858dc2f056c1df2\" style=\"color:#b00012\">\ud83e\udd4e<strong> Which&nbsp;area model represents the factorisation&nbsp;4x<sup>2<\/sup>+8x+3=(2x+3)(2x+1)?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-13.png\" alt=\"\" class=\"wp-image-6494\" style=\"width:337px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-13.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-13-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-13-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-1-4.png\" alt=\"\" class=\"wp-image-6495\" style=\"width:365px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-1-4.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-1-4-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-1-4-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-2-3.png\" alt=\"\" class=\"wp-image-6497\" style=\"width:306px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-2-3.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-2-3-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-2-3-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-3-5.png\" alt=\"\" class=\"wp-image-6499\" style=\"width:385px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-3-5.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-3-5-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-3-5-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<p>This&nbsp;area model represents the factorisation&nbsp;4x<sup>2<\/sup>+8x+3=(2x+3)(2x+1).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__4_-removebg-preview-1.png\" alt=\"\" class=\"wp-image-6503\" style=\"width:345px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__4_-removebg-preview-1.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__4_-removebg-preview-1-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__4_-removebg-preview-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>The&nbsp;left side of the equation represents the total area written as the sum of all the tiles. There are&nbsp;4&nbsp;<em>x<\/em>2&nbsp;tiles,&nbsp;8&nbsp;<em>x<\/em>&nbsp;tiles, and&nbsp;3&nbsp;1&nbsp;tiles, so the sum is&nbsp;4x<sup>2<\/sup>+8x+3.<\/p>\n\n\n\n<p>The&nbsp;right side of the equation represents the total area written as base times height. The base is made up of&nbsp;2&nbsp;<em>x<\/em>&nbsp;tiles and&nbsp;3&nbsp;1&nbsp;tiles, so it is&nbsp;(2x+3).&nbsp;The height is made up of&nbsp;2&nbsp;<em>x<\/em>&nbsp;tiles and&nbsp;1&nbsp;1&nbsp;tile, so it is&nbsp;(2x+1).&nbsp;The base times the height is&nbsp;(2x+3)(2x+1).<\/p>\n\n\n\n<p>The&nbsp;other area models represent factorisations of different&nbsp;polynomials.<\/p>\n\n\n\n<p>This&nbsp;area model shows&nbsp;2x<sup>2<\/sup>+7x+3=(x+3)(2x+1).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__1_-removebg-preview-7.png\" alt=\"\" class=\"wp-image-6504\" style=\"width:380px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__1_-removebg-preview-7.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__1_-removebg-preview-7-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__1_-removebg-preview-7-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>This&nbsp;area model shows&nbsp;4x<sup>2<\/sup>+10x+6=(2x+3)(2x+2).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__2_-removebg-preview-6.png\" alt=\"\" class=\"wp-image-6505\" style=\"width:343px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__2_-removebg-preview-6.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__2_-removebg-preview-6-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__2_-removebg-preview-6-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>This&nbsp;area model shows&nbsp;2x<sup>2<\/sup>+8x+6=(x+3)(2x+2).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__3_-removebg-preview-1.png\" alt=\"\" class=\"wp-image-6507\" style=\"width:332px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__3_-removebg-preview-1.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__3_-removebg-preview-1-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__3_-removebg-preview-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#e8f3ca\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-1634a690f3bd9e99e0a066a33935a400\" style=\"color:#b00012\">\ud83e\udd4e<strong>Which&nbsp;area model represents the factorisation&nbsp;6x<sup>2<\/sup>+9x+3=(2x+1)(3x+3)?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-15.png\" alt=\"\" class=\"wp-image-6513\" style=\"width:309px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-15.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-15-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-15-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-1-5.png\" alt=\"\" class=\"wp-image-6516\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-1-5.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-1-5-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-1-5-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-2-4.png\" alt=\"\" class=\"wp-image-6517\" style=\"width:359px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-2-4.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-2-4-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-2-4-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-3-6.png\" alt=\"\" class=\"wp-image-6521\" style=\"width:371px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-3-6.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-3-6-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-3-6-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<p>This&nbsp;area model represents the factorisation&nbsp;6x<sup>2<\/sup>+9x+3=(2x+1)(3x+3).<\/p>\n<\/div><\/div>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-4-3.png\" alt=\"\" class=\"wp-image-6524\" style=\"width:326px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-4-3.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-4-3-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-4-3-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>The&nbsp;left side of the equation represents the total area written as the sum of all the tiles. There are&nbsp;6&nbsp;<em>x<\/em>2&nbsp;tiles,&nbsp;9&nbsp;<em>x<\/em>&nbsp;tiles, and&nbsp;3&nbsp;1&nbsp;tiles, so the sum is&nbsp;6x<sup>2<\/sup>+9x+3.<\/p>\n\n\n\n<p>The&nbsp;right side of the equation represents the total area written as base times height. The base is made up of&nbsp;2&nbsp;<em>x<\/em>&nbsp;tiles and&nbsp;1&nbsp;1&nbsp;tile, so it is&nbsp;(2x+1).&nbsp;The height is made up of&nbsp;3&nbsp;<em>x<\/em>&nbsp;tiles and&nbsp;3&nbsp;1&nbsp;tiles, so it is&nbsp;(3x+3).&nbsp;The base times the height is&nbsp;(2x+1)(3x+3).<\/p>\n\n\n\n<p>The&nbsp;other area models represent factorisations of different&nbsp;polynomials.<\/p>\n\n\n\n<p>This&nbsp;area model shows&nbsp;9x<sup>2<\/sup>+12x+3=(3x+1)(3x+3).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__5_-removebg-preview-1.png\" alt=\"\" class=\"wp-image-6531\" style=\"width:325px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__5_-removebg-preview-1.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__5_-removebg-preview-1-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__5_-removebg-preview-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>This&nbsp;area model shows&nbsp;3x<sup>2<\/sup>+5x+2=(x+1)(3x+2).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__6_-removebg-preview-2.png\" alt=\"\" class=\"wp-image-6532\" style=\"width:339px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__6_-removebg-preview-2.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__6_-removebg-preview-2-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__6_-removebg-preview-2-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>This&nbsp;area model shows&nbsp;6x<sup>2<\/sup>+7x+2=(2x+1)(3x+2).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__2_-removebg-preview-7.png\" alt=\"\" class=\"wp-image-6534\" style=\"width:340px;height:auto\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__2_-removebg-preview-7.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__2_-removebg-preview-7-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__2_-removebg-preview-7-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">let&#8217;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\/86520\/829\/876\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-166.png\" alt=\"\" class=\"wp-image-9026\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-166.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-166-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-166-150x150.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\/86296\/626\/554\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-171.png\" alt=\"\" class=\"wp-image-9027\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-171.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-171-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-171-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Factorise quadratics using algebra tiles key notes : Understanding Algebra Tiles Algebra tiles are manipulatives that represent algebraic expressions visually. Different tiles represent different terms: Structure of a Quadratic Expression Arranging Tiles to Form a Rectangle Finding the Factors Writing the Factored Form The binomial factors correspond to the dimensions of the rectangle. Example: If<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/y-6-factorise-quadratics-using-algebra-tiles\/\">Continue reading <span class=\"screen-reader-text\">&#8220;Y.6 Factorise quadratics 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-501","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_hostinger_reach_plugin_has_subscription_block":false,"_hostinger_reach_plugin_is_elementor":false,"_links":{"self":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/501","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=501"}],"version-history":[{"count":22,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/501\/revisions"}],"predecessor-version":[{"id":19947,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/501\/revisions\/19947"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=501"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}