{"id":6475,"date":"2014-01-24T17:28:33","date_gmt":"2014-01-24T17:28:33","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6475"},"modified":"2014-12-02T08:26:54","modified_gmt":"2014-12-02T08:26:54","slug":"more-problem-solving-strategies-look-for-a-pattern","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/more-problem-solving-strategies-look-for-a-pattern\/","title":{"rendered":"More Problem-Solving Strategies: Look for a Pattern"},"content":{"rendered":"

Overview:<\/strong><\/p>\n

One of the problem-solving strategies that is often used in math is to look for a pattern.\u00a0 Often when exploring problems, the student can notice a relationship between numbers.\u00a0 This relationship can help to solve the problem by shortening the number of steps it takes to get to a solution.<\/p>\n

Step 1: Make a Table<\/strong><\/p>\n

The first step to look for a pattern is to make a table showing the relationships that are there.\u00a0 For example, suppose the problem were to find the next three numbers in the series 2, 4, 6, 8.\u00a0 They are related in a simple way, such that 2 +2 is 4 +2 is 6 +2 is 8.\u00a0 In order to extend the pattern, 8 +2 is 10, +2 is 12 +2 is 14.\u00a0 Therefore, the next three numbers are 10, 12, and 14.<\/p>\n

Step 2:\u00a0Find the Relationship Between Numbers<\/strong><\/p>\n

In the previous example, the relationship was very simple, as the pattern was the set of the first 7 even numbers.\u00a0 Each number in the series was separated by the same distance.\u00a0 Suppose the relationship weren’t quite as simple.\u00a0 This time, the numbers in the sequence are 1, 5, 14, 30, and 55.\u00a0 What are the next 3 numbers in the series?\u00a0 1 +4 is 5 +9 is 14 +16 is 30 +25 is 55.\u00a0 The numbers aren’t even the same distance from one another.<\/p>\n

Step 3:\u00a0Make a Prediction<\/strong><\/p>\n

What do these numbers have in common?\u00a0 After finding a pattern, it’s possible to predict what the next numbers will be.\u00a0 Those differences 1, \u00a04, 9, 16, and 25, have a pattern in themselves.\u00a0 They are the first 5 squared numbers, as 12<\/sup> is 1, 22<\/sup> is 4, 32<\/sup> is 9, 42<\/sup> is 16, and 52<\/sup> is 25.\u00a0 So the next difference might be 62<\/sup> or 36, and 55 + 36 = 91.\u00a0 The next squared number will be 72<\/sup>, or 49, and 91 +49 = 140.\u00a0 The next squared number will be 82<\/sup> or 64, and 140 + 64 = 204.<\/p>\n

Step 4:\u00a0Check the Answer<\/strong><\/p>\n

The sequence with the next three numbers is 1, 5, 14, 30, 55, 91, 140, and 204.\u00a0 The pattern fits in every step of the sequence.\u00a0 If the numbers were added carefully, it would be easy to check each one, as 1 + 4 is 5, 5 + 9 is 14, 14 + 16 is 30, 30 + 25 is 55, 55 + 36 is 91, 91 + 49 is 140, and 140 + 64 is 204.\u00a0 The next squared number would be 81 (92<\/sup>), and 204 + 81\u00a0is 285.<\/p>\n

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SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Nampa, ID visit: Tutoring in Nampa, ID<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Overview: One of the problem-solving strategies that is often used in math is to look for a pattern.\u00a0 Often when exploring problems, the student can notice a relationship between numbers.\u00a0 This relationship can help to solve the problem by shortening the number of steps it takes to get to a solution. Step 1: Make a […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[13],"tags":[260,658,1078,1079],"class_list":["post-6475","post","type-post","status-publish","format-standard","hentry","category-pre-algebra","tag-check-the-answer","tag-find-the-relationship","tag-make-a-table","tag-make-predictions"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6475","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=6475"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6475\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6475"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6475"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6475"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}