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A Merry Ho Ho Ho and yuletide greetings to Transum users around the world. This is the festive version of the monthly newsletter and begins with a seasonal puzzle.

Santa lives in a region is called Korvatunturi, in Rovaniemi – which is in the Finnish part of Lapland. His house is built with thick walls and small windows to keep out the cold. This year he has decided to make one of the windows twice its original area, but without increasing either its height or width. How can that be done?

The answer is at the end of this newsletter.

"It's beginning to look a lot like Christmas" so this is the perfect time to remind you of Transum’s ChristMaths collection. It gets bigger every year and contains gems that just wouldn’t seem right any other time of year. The first door of the Maths Advent Calendar is now unlocked and this year there’s a new printable ChristMaths card. Enjoy the resources now and during the time left before the season comes to an end.

Subscriber Ann was surprised at how many different expressions containing the digits one to four can be made which equate to twelve. Ann suggested the idea to me and I came up with the 12 Ways of Christmas challenge. You don’t have to do it all in one sitting as the page will remember your attempts so you can dip into it every time you have a spare five minutes.

The Christmas Lesson Starter pages also contain ideas for mathematical Christmas presents and a new suggestion I have for this year is Marcus du Sautoy’s “Thinking Better: The Art of the Shortcut”. I enjoyed listening to him talk about the book on a recent podcast during which he talked about Gauss’ shortcut which I have referred to many times during my teaching career. If you don’t know it I’ll include an excerpt of the transcript here:

*“The story takes us back to Germany in the late 18th century, and a schoolboy named Carl Friedrich Gauss. The young Gauss, sitting — 8, 9 years old in his class, the teacher wants to get a little bit of rest, decides to set them a problem that it will take them ages to actually do. He says ‘You’ve got to add up the numbers from one to 100’. Carl Friedrich Gauss immediately writes down a number on his chalkboard, slams it down on the desk and says, ‘There it is.’”*

If you don’t know Gauss’ shortcut have a look at the Starter called Add ‘Em where there is a big clue.

On the Curriculum page you can now find Schemes of Learning for Year 12 and Year 13 IB Standard level courses. Thanks to my old school for letting me use their sequencing. Click on the blocks to see the resources.

A new Level 2 has been added to the Tree Diagrams exercises along with new exam-style questions. You need to be signed into your Transum account in order to see the worked solutions.

ACTIVITY NUMBER**1000**

The details of each activity stored in a database table is given a unique identification number. In the Starters table these numbers range from 1 to 366 as you would imagine. There is a much bigger table to store the details of all the investigations, exercises and puzzles and I have just created the 1000th record in that table. The thousandth activity is called Percentage Switch, has three levels of difficulty and makes a nice challenge for pupils learning about percentage change.

This month’s puzzle was adapted from one asked by Alex Bellos (taken from Angelo Lewis’ 1893 classic book Puzzles Old and New) in The Guardian online newspaper. Here is the solution that was provided. “The window was diamond-shaped. By enlarging it to a square its area is exactly doubled, without increasing either its height or width. A window shaped as an isosceles or right-angled triangle will equally answer the conditions of the puzzle.”

They have obviously adopted the definition that a diamond is a tilted square rather than a more general rhombus but we understand!

So finally a very happy Christmas to you and those close to you. Stay safe, healthy and happy and look forward to a mathematically exciting 2022.

John

P.S. Calendars, their days are numbered.

Do you have any comments? It is always useful to receive feedback on this newsletter and the resources on this website so that they can be made even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.