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It is said that Father Christmas lives in a magical place near the North Pole. One of the extraordinary facts about this place is that the mean temperature when reported in degrees Celsius is exactly the same number as when reported in degrees Fahrenheit.

The puzzle of the month for December is to figure out what this number is.

This newsletter is for December so may I begin by wishing you a very happy Christmas. Many schools have special festive events in the weeks leading up to Christmas and Mathematics lessons can also have a seasonal theme. Here at Transum Mathematics there is a ChristMaths page linking to all sorts of yuletide flavoured mathematics. One of the time-honoured seasonal mathematical puzzles involves working out the total number of gifts received according to the song 'Twelve Days of Christmas'. If you don't know the song there are many versions of it online but the gist is that the obsessed lover delivers more and more presents on each of the 12 days of the holiday. Pupils are usually able to arrive at the answer themselves but there is no better way to check the answer than with some music. Scroll down the Twelve Days of Christmas Starter page to find a musical excerpt from a Natalie Cole song in which she sings the answer!

The first of the new resources to have appeared on the Transum website this last month is called Don's Graph Snaps. This self-marking exercise is a Transum tribute to the late Don Steward. It appeared on his blog in 2011.

Don was a talented educator, insightful designer of resources and a wonderful person. I worked with Don in the 1990s at Birmingham's Curriculum Support Service. He was the seasoned consultant and I was the new kid on the block. I learned so much from Don and his ideas inspired many of the activities on this website.

Parts of Sequences presents a selection of consecutive terms of a sequence rather than the usual first few terms. The challenge is to choose which given formulas for the nth term matches the sequence fragment. The letters representing the correct formulas produce five five-letter maths words which together make an instruction to perform a calculation in order to claim a trophy.

The Polygon Angles Animation was created to produce the graphics for a new help video but I decided that teachers might also want to use the animation as part of their own explanations. It now resides in the Shine+Write collection. A help video was also made for the Negative Numbers exercise.

Cube Face Meetings and Coloured Cube 3D might just drive you crazy. The ability to relate the faces of a three dimensional cube to the two dimensional representation on a net will hopefully be improved by tackling these exercises. Cutting out nets from paper or card is encouraged!

Trapezium Rule: While working on this brand new self-marking exercise a student asked me what was the ratio of people who called this the Trapezoidal Rule compared to Trapezium Rule. I haven't done the research but I guess it's the same as the Math vs Maths ratio!

Thanks to the teacher for pointing out a slight error in the tessellating challenges involving Pentominoes and Tetrominoes. It has now been corrected. I take consolation in being in good company where understanding tessellations is concerned. I just heard the story on the ‘No Such Thing As A Fish’ podcast of how Marjorie Rice, a mother of five, pointed out an error in Martin Gardner’s work on tessellating pentagons. She worked on the claims Gardner had made in the Scientific American magazine in her free time "by drawing diagrams on the kitchen table when no one was around and hiding them when her husband and children came home, or when friends stopped by.” In February 1976, she sent her discoveries to Gardner who confirmed that she had discovered four new types of tessellating pentagons and over 60 distinct tessellations using pentagons.

It’s a good story that you could share with your pupils. I have included the excerpt in the podcast version of this newsletter.

Breaking News: The first door of the Maths Advent Calendar opened today!

Yet More News: There are now two Maths Christmas Cards ready for printing!

The answer to the puzzle of the month is negative forty. I began with the formula for converting temperatures from Celsius to Fahrenheit:

T (°F) = T (°C) × 9/5 + 32

As the numbers are the same this equation can be solved to find the number, T.

T – 9T/5 = 32

-4T/5 = 32

-4T = 160

T = -40

So the amazing fact is that minus 40 degrees Celsius is exactly the same temperature as minus 40 degrees Fahrenheit. Poor Santa, winter draws on!

Merry Christmas.

John

P.S. If Santa gets too cold this Christmas he could go and sit in the corner, because it is 90 degrees there!

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.