Happy and Unhappy Numbers KS 3 Independent Study

Happy and Unhappy Numbers KS 3 Independent Study Investigation

How the Investigations Work Each Investigation involves two parts 1. Directed tasks These tasks will be very structured and will guide you to research, develop and apply mathematical knowledge and understanding 2. Independent Investigation This will allow you to research your own ideas about the topic. We have suggested some questions or areas that you might like to explore but we encourage you to think of your own too. At the end of this powerpoint there are two slides with some hints to help you get started if you need

How to present your work • We are looking for high quality presentation of your research • The more interesting and inventive the better! • Work can be hand written/drawn, word processed • OR you can present your work in other formats ( a video presentation, a game, a piece of artwork – get creative) • This is a chance for you to show off your skills as an inquisitive mathematician • The Maths department would love to display some of your best work from this project. When you complete your project, please send your work via email to baileyr@laurencejackson. org

Directed Task Happy and Unhappy Numbers We are going to make a chain of numbers starting with 58 using the following rule Rule To find the next number in the sequence, square the digits in your number and add the answers together 58 5² + 8² Continue the sequence: What happens? (hint is on slide 15)

Directed Task Unhappy Numbers The order should be: 58 89 37 145 16 42 4 20

Directed Task 19 1² + 9² Continue the sequence: What happens?

Directed Task Happy Numbers The order should be: 19 82 68 100 1

Independent Investigation Now choose your own starting number. Use the rule to make a number chain. If your chain reaches 1 then all the numbers in the chain are happy numbers If your chain reaches any number in the unhappy circle then all the numbers in the chain are unhappy numbers How many happy or unhappy numbers can you find?

Independent Investigation How many happy or unhappy numbers can you find? 1. Start with the numbers from 1 -100 and work out whether numbers are happy numbers or unhappy numbers. 2. Shade in the happy numbers on the 1 -100 grid. Extension – See if you can make a pattern with your sequences when working out whether numbers are happy or unhappy.

Independent Investigation

Answers

Answers Happy Numbers 91 28 86 19 82 68 100 1 7 49 97 130 10 31 70 94 79 13 32 23 44

Answers 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

66 Answers 72 3 30 57 9 93 47 83 65 90 39 38 74 81 80 18 37 56 88 29 50 43 92 85 17 55 76 145 106 45 63 36 6 98 54 41 162 99 67 89 14 60 77 59 95 42 16 128 96 25 71 61 33 69 58 12 5 34 52 64 84 73 21 46 8 48 75 53 27 22 35 62 117 51 26 15 40 4 20 24 2 87 11 113 78 Unhappy Numbers

Hint 58 5² + 8² 25+64=89 8² + 9²