September 2016 News

If you live in the northern hemisphere you are probably starting a new school year so happy new year to you. Wherever you live you are welcome to the Transum Mathematics newsletter for September 2016. As usual I will begin with the puzzle for this month which is called Separated Twins.

The twins have a safe. The combination of the safe is a six digit number.

Within this six digit number there are two ones separated by one other digit. There are two twos separated by two other digits and there are two threes separated by three other digits.

What is the combination?

As there was no August newsletter there are two months’ worth of new content on the Transum website to tell you about. Let’s begin with the Mathematical Optical Illusions.

This has proved to be a useful visual aid to use while revising some basic geometrical facts with pupils. The illusion bit provides the motivation to study the diagram while you, as the teacher, can sneak in the revision questions such as ‘what is formula for the area of a circle?’, ‘What does arc mean?’ and ‘Name four different types of triangle’. I’m sure you could come up with suitably challenging questions for your pupils as you work your way through the different illusions.

Most Transum subscribers are Secondary/High School teachers but there is a significant proportion of primary teachers too.

This next item is only really relevant to Secondary teachers preparing pupils for GCSE or IGCSE exams. In the UK, next May sees the first of the new style 9 to 1 grade GCSE exams. The Transum think tank has studied the sample assessment materials produced by the exam boards and come up with similar practice questions along with fully worked solutions. These questions have been collected together into 20 practice papers which print nicely onto A4, double sided paper.

One Minute Maths is a hoot! So funny to see good mathematicians making the classic mistake. It’s a bit of fun but highlights a valuable place value, carrying issue. Give it a try (when no one is looking).

Puzzle Cube is a multi-level challenge based on the idea of a Rubik’s-style cube presented as a net. At the time of writing only one person has managed to earn a trophy for the hardest level.

Pupils in general always need more practice with basic mental arithmetic so the more different activities you have to provide that practice the better. Here’s a new two player game for your collection. It’s called Tug of War and has levels for each of the four rules. It can also be played with any of the many Pairs games on the Transum website. Scroll down the Tug of War page to see the links.

You probably already know that there are a range of times tables activities available on the Transum website but Hard Times is new. It is nothing to do with the Charles Dickens novel but is so named as it isolates the hardest times tables facts according the data collected from over ninety thousand trials as can be seen on the Statistics page.

The Calculator Workout page is a visual aid which demonstrates key skills with a common scientific calculator.

The latest pairs game is about Circle Angle Theorems. Not a substitute for practice answering questions and solving problems but a fun support activity.

I hope you enjoy the new activities on Transum.org. Don’t forget that if the website should ever go offline (let’s hope not) you can still get to your favourite activity by using one of the two mirror sites Transum.info and Transum.com. Currently you cannot log in as a subscriber on the mirror sites but if the main site looks as though it will be down for a long time that will change.

The answer to this month’s puzzle is 3 1 2 1 3 2 (or that number with the digits reversed). If you thought it was too easy you can see how this type of puzzle can be extended by looking at the Starter for September 18th.

That’s all for now. Have a worthwhile, satisfying and productive September,

John

Ps The combination locks on safes should really be called permutation locks because it does matter what order the digits are entered.

April 2016 News

Easter has come early this year which means that many schools are currently still closed for the Easter holidays. That’s a pity! It means that you don’t get the opportunity to fool your pupils with the 1st April Starter. Next year maybe?… No, April 1st falls on a Saturday next year. Perhaps you could use the ‘One Out Of Ten’ joke on another day of the year.

The puzzle for this month is about three cars arriving at a three way junction at high speed. The junction has a triangular (ish) traffic island at the centre and each car has a 50% chance of turning left and a 50% chance of turning right when they arrive at the island. What is the probability of no collisions taking place?

March was another busy month for adding content to the website. The most significant addition is Refreshing Revision, the ultimate customisable Starter. It is called Refreshing Revision because every time you refresh the page you get different numbers and diagrams in the questions. Scroll down the page to see and select the concepts you want to be included in the Starter. It should be useable with pupils in Year 5 (with the times tables questions) all the way up to Year 11 (revising for exams).

I will continue to add more concepts to this during this month but if you have any suggestions please let me know.

The leader boards for TablesMaster and Fast Factors have been adapted so that you can filter out all but pupils from your own school. Instructions explaining how to do that are available on the Times Table Filter page. Many thanks to Matt Curtis from Edgewood School for suggesting this idea.

The Times Tables page contains links to many activities pupils can do to improve their recall of multiplication facts. A new activity was created last month called Times Square. It has nothing to do with that famous location in New York but lots to do with providing yet another way for pupils to practise their tables. The completed tables square comes complete with buttons to show some of the geometric patterns created by sets of numbers in the grid.

A number of videos found on YouTube have been added to the curated list but the one that stands out is the one about the mathematical puzzles found in an episode of the Simpsons called Mathlete’s Feat.

I was surprised recently that one of my pupils, who has strong abilities in most areas of mathematics, didn’t know the order of the months of the year. A drag and drop activity was created which he will use as part of his regular recap activities and also help him to remember the number of days in each of the Months of the Year.

Whenever I am teaching probability I would try hard to include a little bit of fun with the Snail Race. It can be adapted to a wide range of abilities and lead to some interesting questions. Last month Ben from New Zealand asked the ultimate question about snail number seven’s chance of winning the race. We have still not been able to come up with the answer but you can follow the discussion on the Snail Race Teacher’s Version page. If you are an expert in Negative Binomial Distributions we need to hear from you!

Previous newsletters can be found with podcasts (the audio versions of the newsletters) online and for the latest news of Transum updates follow @Transum on Twitter. Thanks to all you who have left comments on the Transum web pages and sent feedback about how your pupils have enjoyed using the resources.

Finally the answer to the Tri-junction puzzle. As a subscriber you can see a tree diagram which can be used for solving this puzzle on the Tree Diagrams Challenge page. The answer can be found by considering the probability of all three cars turning left or all three cars turning right. The answer is 0.53 + 0.53 = 0.25 or 25%.

Enjoy the month of April.

John

ps. Parallel lines have so much in common it’s a pity they’ll never meet.

January 2016 News

Happy New Year to you, your family and your pupils. I hope 2016 brings you happiness and that a small part of that happiness comes from your use of the Transum online activities.

We’ll start the year off with a strange puzzle for your pondering pleasure.

• Three ticks are equal to five tocks.
• Two tocks are equal to five tacks.
• Three tacks are equal to one tuck.

Which of the following is the smallest: 1 tick, 2 tocks, 3 tacks or 4 tucks?

While you think about that here is an update of the new activities that appeared on the Transum website last month.

The game Numerate is the numerical version of Scrabble. Players take it in turns to create interconnecting equations on the game board and, in doing so, earn points depending on the complexity and placing of their tiles.

An addictive new grid-shading puzzle called Cryptographic challenges you to find the pictures by using the number string clues at the end of each row and column. The puzzle was created as a child-accessible version of the puzzle included in the Christmas cards sent by the director of GCHQ, Britain’s security and intelligence organisation.

As a Maths teacher, do you know the ultimate, and most probably the first, mathematical riddle? It is about the life of Diophantus, the father of algebra, who lived in the second century. The riddle can be solved by forming and solving an equation containing fractions. You can read more about this on the new “How Old Was Diophantus?” page.

The “Search for Infinity” is a trial-and-improvement challenge in which pupils manipulate Lissajous figures to produce beautiful patterns in their search for the rotated figure-of-eight symbol.

In addition to these new activities many of the existing activities have been added to and improved. I hope they are even more useful supporting your teaching.

If you are based in the UK you will have probably heard the news this week that every child will be expected to know their times tables off by heart when they leave Primary school as part of the Government’s “war on innumeracy”.

Nicky Morgan, the Education Secretary, has unveiled plans to test 11-year-olds on their multiplication skills in new online tests which will be introduced to all Primary schools next year.

There are those, however, who question the necessity of the tests, especially given the costs of administering them. Bafflingly, there is also still a vocal minority who, for one reason or another, believe that children shouldn’t learn their times tables and deride rote learning as having no place in a 21st Century education.

Good Primary teachers know that ‘blended is best’ and that a small amount of rote learning of the multiplication tables pays dividends supporting pupils in other areas of mathematics for the rest of their lives.

On the Transum website, the most popular single activity for many years has been Tablesmaster which is a self-marking online test that encourages pupils to improve their ability to recall their tables so that they can improve their personal best times. The Reverse Bar Chart and Tables Tips add support and motivation though many pupils are more motivated by the High Score Chart.

If you haven’t seen it before, the main Transum Times Tables page provides links to many activities which are very effective in helping children learn their multiplication facts and is just as relevant for Secondary school teachers as for Primary.

The answer to the puzzle for this week can be answered by expressing each thing in terms of tocks:

• 1 tick = 5/3 tock
• 2 tocks = 2 tocks
• 3 tacks = 6/5 tock
• 4 tucks = 24/5 tock

So the smallest is 3 tacks.

That’s all for this month.

John

ps . Why did the (x2+1) tree fall over?

Because it had no real roots.

May 2015 News

It’s an old joke but this newsletter is being written on Star Wars Day, ‘May The Fourth Be With You!’

The puzzle for this month is not, on the surface, strictly mathematical but, as you’ll see from the answer at the end of this newsletter, there is some mathematical debate as to the correct answer. It is however a puzzle that can keep you thinking throughout the day and keep your mind active during coffee breaks, jogging sessions or when the output of the TV is not really very engaging.

Here it is. Find the number which when written as a word has all the letters in alphabetical order and then find the first number to contain the letter A.

Mystic Rose

The first activity worth mentioning this month is called Mystic Rose. It’s an old idea made interactive. It initially seems as though the number sequence created by the number of regions in the roses is simply powers of two but as you get to the 6th term of the sequence there is a surprise in store.

This activity comes with some printable sheets which makes the counting process a lot easier. The sheets can also be used for other investigations such as the two-colour theorem or finding polygons in the patterns of lines. This activity can produce some stunning display work.

The ‘Learn a times table in five days’ page has been brought up to date with a reorganising of the activities and cartoon-like pictures added for all 121 multiplication facts. These pictures, designed to help a person remember whichever multiplication fact they can’t get into their heads, are collected into an easily accessible click grid for Transum subscribers.

The Tablesmaster results page has also been updated so that a pupil can see the memory-aiding picture for the multiplication fact that took longest to recall. I hope this addition contributes towards times table learning around the world.

For those of you working in an IB school you may be interested to hear that additional worked solutions have been added to the Exam-Style Questions pages. Most of the worked solutions contain relevant TI-nSpire screen shots. It is hoped this resource will be just as useful for A-level teachers as the content is so similar.

Finally the answer to the puzzle. Forty is the number that has its letters in alphabetical order and the first number to contain the letter A is either a thousand or one hundred and one. You can see the discussion this puzzle generated on the 7th October Starter page.

Good luck to everyone involved in this exam season. Just remember that Transum has some less demanding, fun activities for you to enjoy when it is all over.

John

ps.If it is cold, go and stand in the corner, because it is 90 degrees there!

March 2015 News

Welcome to the March 2015 edition of the Transum Mathematics Newsletter. This month the focus is on probability and the puzzle for this month is one that all Maths teachers will probably (?) know the answer to. What is the minimum number of pupils there needs to be in a class such that the probability of two or more of them having the same birthday is greater than a half? If you don’t know have a guess (make an estimate).

The answer is at the end of this newsletter but for now let’s look at what was new or updated on the Transum website last month.

The copyright holders of the puzzles Suko and Sujiko granted Transum permission to create versions of the puzzles online. The Transum version allows the user to have up to 5 clues to help find the solution. This allows the puzzles to be used with classes of different abilities as the teacher can decide just how difficult each puzzle should be.

Beat the Clock is great fun no matter how good your numeracy skills are. Race to answer the mental arithmetic questions as a curtain slowly lowers concealing the questions on the screen. There are nine levels of difficulty but you can make the challenge easier by choosing to only answer the questions in the left column.

Assuming your school does not have a policy of using traditional playing cards in the classroom you’ll find they are a versatile resource for mathematical activities. Visit the new Playing Card Maths section of the website to see all the ideas that have been gathered together so far. Please get in tough if you have any other suggestions. If you are a one-to-one Maths Tutor you may want to always have a pack of cards in your bag as a plan ‘B’ just in case the other activities you have planned for the tutorial go horribly wrong.

If you are interested in times table skills I’m sure you are aware of one of the most popular Transum activities called TablesMaster. Now when you claim your trophy for completing an exercise you have the option to view your very own ‘reverse bar chart’, comparing your trophy winning times for each of the times tables. It has proved to be a great motivator for pupils working on their times tables.

Other less newsworthy activities have been added to the site and many updated but you’ll probably come across those when you browse the topic index.

Probability is a unique topic in the school mathematics syllabus. As well as learning the techniques, formulas and procedures pupils should develop a ‘feel’ for what probability means. Most adults have a limited understanding of the concept and would think that if they had tossed a coin nine times and it had landed heads each time that the probability of the tenth toss landing tails is more likely as it hasn’t happened for so long! So does the coin have a memory? Does it know that if it has landed heads many times that it should be time to give tails a chance? No of course not. The probability is still 50% (unless the coin is biased in some way).

There are some nice examples of probability in the real world I have just been listening to on the excellent podcast called ‘No Such Thing As A Fish’. The QI Elves tell of how Spotify changed its random play list because people didn’t think it really was random enough! You can hear that excerpt as part of the Transum Podcast for this month.

The surprising answer to this month’s question is that there need only be 23 pupils for the probability of two or more of them to have the same birthday to be greater than a half! The reason is well documented on the web and in particular in an article called ‘The Birthday Problem’ on Wikipedia. If you’d like to try to prove it yourself you may want to consider the question of the birthdays not being on the same day and subtract your result from one. Good Luck.

John

ps 3.14% of Sailors are PI rates!

February 2015 News

This is the February 2015 Transum Newsletter bringing you the latest news from Transum Mathematics.

During this past month I have been to the cinema and seen ‘The Imitation Game’ about the code cracking achievements of Alan Turing. I’m sure you are familiar with the story and a key mathematical feature of it is the design of the computer built to crack the ‘Enigma’.

An Enigma machine was a coding device invented in Germany at the end of world war 1. The total number of possible ways in which an Enigma machine could be set up was 158 million million million. This month’s puzzle takes that idea as its theme.

Consider a small part of the alphabet, just the vowels. How many ways can you create a code for the vowels by assigning to each vowel a different vowel?

The answer is at the end of this newsletter but if the idea of breaking codes interest you don’t miss the online code cracking activities on the Transum website.

As usual a number of people have sent in comments and observations during the last month.

On the subject of the Squared Animals starter Faye Harris from O.L.S.T says “We struggled with this problem until we realized the squares could be at different angles.” And Mr.T from Manchester Health Acadamy says “Please could someone tell me how to he 4×4 with 5 squares, so I can explain to my class. Thank you!”

Regarding the Light Shopping starter Nick G from Ireland says “This is driving me and my class nuts!” and Miss Karen from Hong Kong says “We had one smart student who got it but the class thought it was tricky!”

Finally a comment about the Anagrams starter. A number of mathematical words have had their letters mixed up and one of those words is ‘survey’. Brogan from Paisley Grammar says “To be honest, survey is not maths related.”. Do you agree?

During last month we welcomed new subscribers from the United Kingdom, United States and from one of the International schools in Thailand. You are all very welcome.

January has been a busy month for updating and adding new material to the website. Noteble additions include: Polygon Pieces (the higher levels are surprisingly difficult while Level one would be suitable for young children), Misfits (based on a board game I had as a child), Discombobulated (a basic addition challenge and a race against time) and two more pairs games designed to help pupils recognise the simple area and volume formulae and the names for parts of a circle.

The current times tables news is that after 33,527 timed test results have been collected it is clear that two times eleven takes the least amount of thinking time while nine times twelve takes the most. You can see the statistics here.

Finally the answer to this month’s puzzle is 44. Many people may have got the wrong answer (120) if they missed the stipulation that each vowel has to be coded by a ‘different’ vowel.

Here are all the ways the vowels a, e, i, o and u can be coded:

e, a, o, u, i
e, a, u, i, o
e, i, a, u, o
e, i, o, u, a
e, i, u, a, o
e, o, a, u, i
e, o, u, a, i
e, o, u, i, a
e, u, a, i, o
e, u, o, a, i
e, u, o, i, a
i, a, e, u, o
i, a, o, u, e
i, a, u, e, o
i, o, a, u, e
i, o, e, u, a
i, o, u, a, e
i, o, u, e, a
i, u, a, e, o
i, u, e, a, o
i, u, o, a, e
i, u, o, e, a
o, a, e, u, i
o, a, u, e, i
o, a, u, i, e
o, i, a, u, e
o, i, e, u, a
o, i, u, a, e
o, i, u, e, a
o, u, a, e, i
o, u, a, i, e
o, u, e, a, i
o, u, e, i, a
u, a, e, i, o
u, a, o, e, i
u, a, o, i, e
u, i, a, e, o
u, i, e, a, o
u, i, o, a, e
u, i, o, e, a
u, o, a, e, i
u, o, a, i, e
u, o, e, a, i
u, o, e, i, a

Have a good February.

John

ps Why do you rarely find mathematicians spending time at the beach? The answer is because they have sine and cosine to get a tan and don’t need the sun!