Happy Numbers

Some numbers are happy and others are not!

To find out whether a number is happy, square each of its digits, add the answers and repeat. If you end up with 1 the number is happy!

How many happy numbers can you find?

E.g. Consider 19

12 + 92 = 82
82 + 22 = 68
62 + 82 = 100
12 + 02 + 02 = 1

This shows that 19 is a happy number.

A Mathematics Lesson Starter Of The Day

Topics: Starter | Arithmetic | Investigations

  • C R Walters, Drayton School Oxfordshire
  • Make it so tht you can flick from day to day while on the page of one particular starter. Also have some way of knowing what date you are on while on a page - in case you want to use a starter from another day
  • Transum,
  • Good Idea. I have now put navigation links as you suggested at the top of this box. I hope this makes it easier for you to get around. Enjoy the Starters,
  • Wikipedia,
  • In the Doctor Who episode "42", a sequence of happy prime numbers is used as a code for unlocking a sealed door on a spaceship falling into a star, namely 313, 331, 367 and 379.
  • Miss Irons, Blean, Kent
  • One of my class wants to know if decimal numbers count. 0.1 should be ok but your tester can't cope!
  • Transum,
  • Sorry Miss Irons. Decimal numbers are not considered to be particularly happy though it was good of your class to be thinking about them. Perhaps your class could come up with a special name for happy decimals?
  • Primary 7, Bargeddie Primary School
  • Several of our class (Ellie, Thomas, Callum and Nicole) noticed that any numbers made up of 1 followed by any number of zeros e.g. 10, 100, 1000, 10000000, 100000000 etc.! would always be a happy number! :-).
  • Inspiring Maths, Twitter

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
Click here to enter your comments.

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Laptops In Lessons

Teacher, do your students have access to computers such as tablets, iPads or Laptops?  This page was really designed for projection on a whiteboard but if you really want the students to have access to it here is a concise URL for a version of this page without the comments:


However it would be better to assign one of the student interactive activities below.

Laptops In Lessons

Here is the URL which will take them to an interactive Happy Numbers activity.


Student Activity



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