{"id":62750,"date":"2021-04-01T15:54:30","date_gmt":"2021-04-01T10:24:30","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=62750"},"modified":"2022-04-01T10:26:07","modified_gmt":"2022-04-01T04:56:07","slug":"eureka-math-grade-5-module-6-lesson-31","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/eureka-math-grade-5-module-6-lesson-31\/","title":{"rendered":"Eureka Math Grade 5 Module 6 Lesson 31 Answer Key"},"content":{"rendered":"

Engage NY Eureka Math 5th Grade Module 6 Lesson 31 Answer Key<\/h2>\n

Eureka Math Grade 5 Module 6 Lesson 31 Problem Set Answer Key<\/h3>\n

\"Engage
\nAnswer :
\n\"Engage-NY-Eureka-Math-5th-Grade-Module-6-Lesson-31-Answer-Key-Eureka-Math-Grade-5-Module-6-Lesson-31-Problem-Set-Answer-Key\"<\/p>\n

Eureka Math Grade 5 Module 6 Lesson 31 Reflection Answer Key<\/h3>\n

Today, when we saw a video on the Fibonacci sequence in the spiral and in nature, it may have felt a bit like \u201cmath magic.\u201d Have you ever felt math magic in your elementary school years? If so, when did you experience it? If not, did you experience it today? Explain.
\nAnswer:
\nYes , It is math magic .
\nExplanation :
\nThe\u00a0Fibonacci sequence\u00a0is a series of\u00a0numbers\u00a0where a\u00a0number\u00a0is the addition of the last two\u00a0numbers, starting with 0, and 1. The\u00a0Fibonacci Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55\u2026
\nwe look for patterns as
\nThe\u00a0brain looks for patterns\u00a0and fills in the blanks. It uses\u00a0patterns\u00a0to understand the relationship between things\u2014putting them in context. \u201cThe\u00a0human brain\u00a0is a\u00a0pattern-recognition machine. … They are learning\u00a0patterns\u00a0and developing rules that guide\u00a0their\u00a0decision and make them faster and more accurate.\u201d<\/p>\n

Eureka Math Grade 5 Module 6 Lesson 31 Homework Answer Key<\/h3>\n

Question 1.
\nList the Fibonacci numbers up to 21, and create, on the graph below, a spiral of squares corresponding to each of the numbers you write.
\n\"Eureka
\nAnswer:
\n\"Engage-NY-Eureka-Math-5th-Grade-Module-6-Lesson-31-Answer-Key-Eureka-Math-Grade-5-Module-6-Lesson-31-Homework-Answer-Key\"
\nExplanation :
\nThe\u00a0Fibonacci Sequence can be written as a “Rule
\nThe Rule is\u00a0xn<\/sub>\u00a0= xn\u22121<\/sub>\u00a0+ xn\u22122
\n<\/sub>First, the terms are numbered from 0 onwards like this:<\/p>\n

\n\n\n\n\n
n =<\/i><\/td>\n0<\/i><\/td>\n1<\/i><\/td>\n2<\/i><\/td>\n3<\/i><\/td>\n4<\/i><\/td>\n5<\/i><\/td>\n6<\/i><\/td>\n7<\/i><\/td>\n8<\/i><\/td>\n9<\/i><\/td>\n10<\/i><\/td>\n11<\/i><\/td>\n12<\/i><\/td>\n13<\/i><\/td>\n14<\/i><\/td>\n15<\/i><\/td>\n<\/tr>\n
xn<\/sub>\u00a0=<\/td>\n0<\/td>\n1<\/td>\n1<\/td>\n2<\/td>\n3<\/td>\n5<\/td>\n8<\/td>\n13<\/td>\n21<\/td>\n34<\/td>\n55<\/td>\n89<\/td>\n144<\/td>\n233<\/td>\n377<\/td>\n392<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

So term number 6 is called <\/span>x6<\/sub><\/span>\u00a0(which equals 8).<\/span><\/p>\n<\/div>\n

\n\n\n\n
Example: the\u00a08th\u00a0term is
\nthe\u00a07th\u00a0term plus the\u00a06th\u00a0term:<\/p>\n

x8<\/sub>\u00a0= x7<\/sub>\u00a0+ x6<\/sub><\/span><\/p>\n<\/td>\n

\"fibonacci<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

So we can write the rule:
\nThe Rule is\u00a0xn<\/sub>\u00a0= xn\u22121<\/sub>\u00a0+ xn\u22122
\n<\/sub>where:
\nxn<\/sub>\u00a0is term number “n”
\nxn\u22121<\/sub>\u00a0is the previous term (n\u22121)
\nxn\u22122<\/sub>\u00a0is the term before that (n\u22122)<\/p>\n

Question 2.
\nIn the space below, write a rule that generates the Fibonacci sequence.
\nAnswer:
\nThe\u00a0Fibonacci Sequence can be written as a “Rule
\nThe Rule is\u00a0xn<\/sub>\u00a0= xn\u22121<\/sub>\u00a0+ xn\u22122<\/sub><\/p>\n

Question 3.
\nWrite at least the first 15 numbers of the Fibonacci sequence.
\nAnswer:
\nThe\u00a0Fibonacci Sequence can be written as a “Rule
\nThe Rule is\u00a0xn<\/sub>\u00a0= xn\u22121<\/sub>\u00a0+ xn\u22122<\/sub>
\nThe first 15 numbers of the Fibonacci sequence are :<\/p>\n\n\n\n\n
n =<\/i><\/td>\n0<\/i><\/td>\n1<\/i><\/td>\n2<\/i><\/td>\n3<\/i><\/td>\n4<\/i><\/td>\n5<\/i><\/td>\n6<\/i><\/td>\n7<\/i><\/td>\n8<\/i><\/td>\n9<\/i><\/td>\n10<\/i><\/td>\n11<\/i><\/td>\n12<\/i><\/td>\n13<\/i><\/td>\n14<\/i><\/td>\n15<\/i><\/td>\n<\/tr>\n
xn<\/sub>\u00a0=<\/td>\n0<\/td>\n1<\/td>\n1<\/td>\n2<\/td>\n3<\/td>\n5<\/td>\n8<\/td>\n13<\/td>\n21<\/td>\n34<\/td>\n55<\/td>\n89<\/td>\n144<\/td>\n233<\/td>\n377<\/td>\n392<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"

Engage NY Eureka Math 5th Grade Module 6 Lesson 31 Answer Key Eureka Math Grade 5 Module 6 Lesson 31 Problem Set Answer Key Answer : Eureka Math Grade 5 Module 6 Lesson 31 Reflection Answer Key Today, when we saw a video on the Fibonacci sequence in the spiral and in nature, it may … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/62750"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=62750"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/62750\/revisions"}],"predecessor-version":[{"id":91569,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/62750\/revisions\/91569"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=62750"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=62750"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=62750"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}