{"id":227195,"date":"2025-06-06T03:10:30","date_gmt":"2025-06-06T03:10:30","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=227195"},"modified":"2025-06-06T03:10:34","modified_gmt":"2025-06-06T03:10:34","slug":"carson-uses-cubes-to-make-a-pattern-of-shapes","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/06\/carson-uses-cubes-to-make-a-pattern-of-shapes\/","title":{"rendered":"Carson uses cubes to make a pattern of shapes"},"content":{"rendered":"\n

Carson uses cubes to make a pattern of shapes. The first shape has a height of 2 cubes and a length of 2 cubes, as shown below. For each step in the pattern, Carson adds 1 cube to the height and 1 cube to the length. Which sentence about the shapes in Carson’s pattern is true? Step 1 height length The total number of cubes in each shape will be even. The total number of cubes in each shape will alternate between even and odd. The length of each shape will alternate between even numbers and odd numbers. The length of each shape will be an even number<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Correct Answer:<\/strong>
The length of each shape will alternate between even numbers and odd numbers.<\/strong><\/p>\n\n\n\n

\n\n\n\n

Explanation<\/strong><\/h3>\n\n\n\n

The problem describes a pattern of shapes made from cubes. In Step 1, the shape has a height of 2 cubes<\/strong> and a length of 2 cubes<\/strong>. With each step in the pattern, Carson adds 1 cube to the height and 1 cube to the length<\/strong>. This means:<\/p>\n\n\n\n

    \n
  • Step 1:<\/strong> Height = 2, Length = 2<\/li>\n\n\n\n
  • Step 2:<\/strong> Height = 3, Length = 3<\/li>\n\n\n\n
  • Step 3:<\/strong> Height = 4, Length = 4<\/li>\n\n\n\n
  • Step 4:<\/strong> Height = 5, Length = 5<\/li>\n\n\n\n
  • \u2026 and so on.<\/li>\n<\/ul>\n\n\n\n

    Let\u2019s examine the lengths<\/strong> over multiple steps:<\/p>\n\n\n\n

      \n
    • Step 1: Length = 2 \u2192 Even<\/li>\n\n\n\n
    • Step 2: Length = 3 \u2192 Odd<\/li>\n\n\n\n
    • Step 3: Length = 4 \u2192 Even<\/li>\n\n\n\n
    • Step 4: Length = 5 \u2192 Odd<\/li>\n<\/ul>\n\n\n\n

      As seen here, the length alternates between even and odd numbers<\/strong> with each step. This is because Carson adds 1 cube to the length<\/strong> each time, and increasing any number by 1 always switches its parity (even to odd or odd to even). Therefore, the correct statement is:
      \u201cThe length of each shape will alternate between even numbers and odd numbers.\u201d<\/strong><\/p>\n\n\n\n

      Let\u2019s also briefly examine the other options<\/strong>:<\/p>\n\n\n\n

        \n
      1. \u201cThe total number of cubes in each shape will be even.\u201d<\/strong>
        \u274c Not true \u2014 the total number of cubes increases by 2 each step (1 in height and 1 in length), so it alternates between even and even if it starts from an even number (2+2 = 4). But the arrangement doesn\u2019t guarantee the total<\/strong> stays even consistently.<\/li>\n\n\n\n
      2. \u201cThe total number of cubes will alternate between even and odd.\u201d<\/strong>
        \u274c Also incorrect, because increasing by 2 keeps parity the same.<\/li>\n\n\n\n
      3. \u201cThe length will always be even.\u201d<\/strong>
        \u274c False \u2014 it alternates between even and odd.<\/li>\n<\/ol>\n\n\n\n

        \u2705 Correct choice: \u201cThe length of each shape will alternate between even numbers and odd numbers.\u201d<\/strong><\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        Carson uses cubes to make a pattern of shapes. The first shape has a height of 2 cubes and a length of 2 cubes, as shown below. For each step in the pattern, Carson adds 1 cube to the height and 1 cube to the length. Which sentence about the shapes in Carson’s pattern is […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-227195","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227195","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=227195"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/227195\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=227195"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=227195"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=227195"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}