# December 2015 News

Happy Christmas. This is the December Transum newsletter coming to you with lots of festive cheer and good wishes for the future.

Here is the puzzle for this month. Noel and Merrie received some Christmas presents. The number of presents Noel received was a power of 3. The number of presents Merrie received was a power of 2. The number of Christmas presents they received were consecutive numbers and less than ten. How many presents did they receive?

You will probably arrive at a first answer fairly quickly but there are actually four different answers. Can you find all four? The answers will be given at the end of this newsletter after a rundown of the notable new features on the Transum website.

Although they are not a new idea, many teachers have never used mini whiteboards in class. The fact is that most classrooms are more likely to have pupils with computing devices than mini whiteboards so this simple facility allows you to make alternative use of the devices. Pupils write or draw their answer to plenary questions on this whiteboard simulator then hold up their devices so the teacher can see. This is a much better idea than putting hands up! This way the teacher can instantly see what everyone is thinking rather than just one person.

I would like to say that I am surprised that the Broken Chessboard Puzzle has been completed by so many people. The puzzle was first made popular by Henry Ernest Dudeney (1857 – 1930) who was an English author and mathematician. The puzzle appeared in his book ‘The Canterbury Puzzles and Other Curious Problems’ in 1907. I thought solving the puzzle would be too difficult for most people but I have been proved wrong. Congratulations to all those people who have earned a trophy for finding a correct solution.

The Starters for 6th March and 4th December have both been replaced with new ideas. The first is the Goat Grazing situation I have used for decades to introduce the topic of Loci. The latter challenges pupils to imagine a dice reflected in two mirrors. Quite a challenge for many.

The number of printable worksheets available only to subscribers is rapidly increasing. Even in these days of hi-tech it a good idea to provide variety to the learning experience with more practical activities particularly relevant to some Maths topics more than others.

Finally I would like to say how much I have enjoyed a new app I downloaded (free) to my iPad. It is called Sumaze and has been produced by MEI. Perfect for Year 12 students who need practice with inequalities, the modulus function, indices, logarithms and primes. It is also useful lower down the school but certain sections such as the logarithm puzzles would of course be inaccessible. Solving the thoughtfully constructed puzzles brings an enhanced understanding of the basic mathematical concepts in a fun setting. I’m stuck on the final level in Fermat’s Room so any suggestions gratefully received.

Are you having a problem thinking what to write in the Christmas cards you are sending to your Maths teacher colleagues? How about this:

It reads ‘Complements of the (Cs) season (2u) to you’.

Talking of Christmas and puzzles, here are the four answers to this month’s seasonal puzzle which is also the Starter for 16th December and called The Power of Christmas:

Have a happy and merry Christmas and enjoy the Transum festive activities.

John

ps Q. Why did the pupil get closer to the fireplace when doing Maths homework?

# December 2014 News

Dear All,

This months’ newsletter is a few days early due to an email received from Fox News but more about that later.

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 linked 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!

Last week I received an email from the Fox News and Business Network in New York. They were asking for permission to use a diagram on Transum Mathematics in a forthcoming news programme. Unfortunately the numbers on the diagram were made-up figures for illustrative purposes only so it seemed the time was right to gather some real data. That is the reason this newsletter is being sent early. I would like to ask you to add to the data before the broadcast next week. I haven’t told you exactly the mathematical twist here but that will become evident when you answer the eight very simple questions:

… and if you could get your pupils to answer the questions online too that would be a real bonus!

The most surprisingly successful new activity on Transum Mathematics is the Dump-A-Dice Race game. It is designed for pupils needing practice recognising square and prime numbers up to 100 (that’s everyone isn’t it?) and is presented in the form of an online board game. It can be played by up to four players so provides an ideal opportunity to break from individual work. As the name suggests, the moves are determined by rolling online dice but, so that it is not purely a game of chance, three dice are rolled and the player has to decide which two should provide the total for their move. This means that skill is involved as the players have to choose the best way trough the numbered stepping stones.

The True Or False activity was updated. The updating process did reveal a couple of interesting thoughts. Would your pupils be able to sketch an irregular hexagon in which all of the external angles were 60 degrees? Also would they think a semicircle has to have a diameter as one of its sides or could a circle be cut into two equal area semicircles using a wavy line?

In addition to many pages on the website being updated, Matchstick Patterns has been added and in the next few days a new series of exercise on algebraic fractions will appear. Please let me know if you have any suggestions for new activities.

Many comments were received this month prompted by the Firewords starter with lots of new words being found.

On the subject of the Ice Cream starter, Dr Duxbury from Edwinstree Middle School says “A rather ambiguous question! Does ‘different’ mean you cannot have the same flavour twice (e.g. two strawberry scoops which I like) or that you count strawberry on the bottom and chocolate on top the same as chocolate on the bottom and strawberry on top (most ice-cream sellers rarely put the ice-cream side by side!). Do you have to have two scoops or can you have just one scoop? Many assumptions made here which makes for a very good discussion with your class where they can find a variety of answers! At the end of the day as long as students can justify and explain their answers, this is all that matters.”

After trying the Five Digits starter Glen from Brentwood says “I would argue that a multiple mode solution, e.g. {2,2,3,3,5}, is a contradiction. I.e. the mode equals the mean, and the mode does not equal the mean. I would also argue for allowing {0,0,0,0,0} as a solution. Our results are: {0,0,0,0,0}, {1,2,2,2,3}, {2,4,4,4,6}, {3,6,6,6,9}, {2,5,5,6,7}, {3,4,5,5,8}. Nice problem, thanks.”

Year 5 from Middlemarch School tried the activity called Satisfaction. The task, as it stands is impossible, but it certainly generates a great deal of mathematical thinking, reasoning and hypothesising. They say “We got 12 numbers on the grid and we are only Year 5! It should be called UNSATISFACTION.”

Finally, on the subject of the Wordles starter, JW from Luton says “Realised I could use this to prompt meaning of unfamiliar words/phrases, and maybe use the same idea to get the students to produce wall displays – to help them in class, and other students too.”

Thanks everyone for their comments, keep them coming!