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
1^{2} + 9^{2} = 82
8^{2} + 2^{2} = 68
6^{2} + 8^{2} = 100
1^{2} + 0^{2} + 0^{2} = 1
This shows that 19 is a happy number.
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Topics: Starter  Arithmetic  Investigations
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Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon search box and some items chosen and recommended by Transum Mathematics to get you started.
Have you read Craig's book yet?Craig Barton must surely be the voice of Mathematics teachers in the UK. His wonderful podcasts interviewing the industry experts have culminated in this wonderful book. As Craig says: "I genuinely believe I have never taught mathematics better, and my students have never learned more. I just wish I had known all of this twelve years ago..." more... "How I wish I’d taught maths' is an extraordinary and important book. Part guide to research, part memoir, part survival handbook, it’s a wonderfully accessible guide to the latest research on teaching mathematics, presented in a disarmingly honest and readable way. I know of no other book that presents as much usable research evidence on the dos and don’ts of mathematics teaching in such a clear and practical way. No matter how long you have been doing it, if you teach mathematics—from primary school to university—this book is for you." Dylan Wiliam, Emeritus Professor of Educational Assessment, UCL. 
Casio Classwiz CalculatorThere is currently a lot of talk about this new calculator being the best in its price range for use in the Maths classroom. The new ClassWiz features a highresolution display making it easier to view numerical formulas and symbols but it isn't a graphical calculator as such (it has the capacity to draw graphs on your smart phone or tablet, via a scannable QR code and an app). As well as basic spreadsheet mode and an equation solving feature you also get the ability to solve quadratic, cubic or quartic polynomial inequalities and the answer is given just as it should be written down, using the correct inequality symbols! This calculator has a highperformance processor and twice the memory of previous models ensuring speedy operation and superior computational power.more... 
Texas Instruments Nspire CalculatorThis handheld device and companion software are designed to generate opportunities for classroom exploration and to promote greater understanding of core concepts in the mathematics and science classroom. TINspire technology has been developed through sound classroom research which shows that "linked multiple representation are crucial in development of conceptual understanding and it is feasible only through use of a technology such as TINspire, which provides simultaneous, dynamically linked representations of graphs, equations, data, and verbal explanations, such that a change in one representation is immediately reflected in the others. For the young people in your life it is a great investment. Bought as a gift for a special occasion but useful for many years to come as the young person turns into an Alevel candidate then works their way through university. more... 
iPad AirThe analytics show that more and more people are accessing Transum Mathematics via an iPad as it is so portable and responsive. The iPad has so many other uses in addition to solving Transum's puzzles and challenges and it would make an excellent gift for anyone. You have to hold iPad Air to believe it. It’s just 7.5 millimeters thin and weighs just one pound. The stunning Retina display sits inside thinner bezels, so all you see is your content. And an incredible amount of power lies inside the sleek enclosure. So you can do so much more. With so much less. more... Before giving an iPad as a gift you could add a link to iPad Maths to the home screen. 
Click the images above to see all the details of these items and to buy them online.
Teacher, do your students have
access to computers? 

Here a concise URL for a version of this page without the comments.
Transum.org/go/?Start=January25
Here is the URL which will take them to an interactive Happy Numbers activity.