# Calculator Keys at the Corners of a Rectangle

Welcome to the Transum newsletter for November 2018. Here is this month’s puzzle.

Type a four digit number on to your calculator. The keys used to type in this number must form a rectangle. Each digit should be one of the corners of this rectangle and you can work your way around this rectangle either clockwise or anticlockwise starting at any corner of the rectangle.

After you have created many four-digit numbers using this method you should see that all of the numbers have something in common. They are all divisible by the same prime number. What is that number? The answer is at the end of this newsletter.

Now I am excited to tell you about the new additions to the Transum website that appeared during October.

Venn Paint Level 3: Shading areas of Venn diagrams is much better done using this web page rather than paper and crayons as you’ll find the undo button very useful. Levels one and two have been popular for a number of years now but yesterday I added a level three which contains some of the more unusual looking Venn diagrams.

Venn diagrams were introduced to the world by mathematician John Venn (1834 – 1923). What is less well known is that he also built rare machines. One of his machines was designed to bowl cricket balls. It was so fascinating that when Australian cricketers were visiting Cambridge, the machine was used to entertain them and it actually bowled out the top ranked player of the team four times consecutively!

Cylinders: A new multi-level online exercise requiring pupils to apply formulae for the volumes and surface areas of cylinders to answer a wide variety of questions starting with the routine and going on to more complex problem-solving experiences.

Fractions by Wholes: Although there are already many fraction activities on the site this new exercise has its niche. It is a three-level set of exercises on multiplying and dividing proper fractions and mixed numbers by whole numbers. As an added bonus jigsaw pieces are awarded for each correct answer and these pieces can be dragged to form a picture containing a mathematical joke.

Pascal’s Triangle: Get to know this famous number pattern with some revealing learning activities ranging from filling in a partially completed triangle to colouring in multiples to reveal beautiful patterns.

Pascal’s Christmas Tree: Following on from the previous activity and introducing a festive theme, this fun interface allows pupils to light up the Christmas tree by flashing numbered lights according their own number patterns.

Last week while on one of my regular park runs I enjoyed listening to a podcast by Grammar Girl. The presenter, Mignon Fogarty, explained that numbers do not exist in all cultures. There are numberless hunter-gatherers embedded deep in Amazonia, living along branches of the world’s largest river tree. Instead of using words for precise quantities, these people rely exclusively on terms analogous to “a few” or “some.” For the bulk of our species’ approximately 200,000-year lifespan, we had no means of precisely representing quantities. What’s more, the 7,000 or so languages that exist today vary dramatically in how they utilise numbers.

Mignon explores the ways in which humans invented numbers, and how numbers subsequently played a critical role in other milestones, from the advent of agriculture to the genesis of writing. If you would like to know more about this you can find it at  Grammar Girl episode 642. The podcast takes its information from a book called Numbers and the Making of Us.

The answer to the puzzle of the month is eleven. Subscribers can see the proof of this fact on the Advanced Starter page called Key Eleven.

That’s all for now

John

PS. I could tell you a joke about 288… But I won’t as it is two gross!

# 31 Oct = 25 Dec

A very warm welcome to the Transum Mathematics newsletter for October 2018.

It begins with the puzzle of the month.

Five friends are talking about their house numbers. They work out that the mean is five, the mode is two, and the median is six. What are the five house numbers?

September was another busy month for updating and adding to the activities on the website. Here are some of the highlights:

Pancake Day is a new interactive puzzle with a low threshold and high ceiling. The objective is to use the spatula (a drag and drop image) to toss the pancakes a number of times so that they end up in a pile sorted according to their size.

In addition to getting the pancakes sorted pupils could describe the algorithm or series of steps required to sort pancakes whatever their initial positions. A much more advanced to challenge is to work out the minimum number of moves for each pile. This is quite a challenging task and most probably beyond the scope of school mathematics but interesting nevertheless.

Fraction Dissect has proved to be a very popular exercise so a Level 3 has been added. This level features circles in which a number of parts have been shaded. The task is to calculate the fraction of the whole circle that has been coloured in.

Unit Pricing is a set of five exercises preparing pupils to calculate best buys, a useful skill indeed. Correct answers to each of the questions in levels one to three earn jigsaw pieces which, when all collected, fit together to make an extremely hilarious mathematical joke. Levels four and five are drag-and-drop shopping trolley activities with more complex situations.

Cosmic Redshift is a strange name for a mathematical activity but to explain it would be to give away the puzzle’s hidden secret. Pupils are asked to work their way through a flowchart with a number of their choosing. They should find that they always get the same answer but why? That sounds like a prompt for an investigation! As always the answer is available to Transum subscribers lower down the page.

Here’s an update on the Trafalgar Square puzzle which you may have read about in the last newsletter. The creators, two Slovakian brothers have been in touch. They were pleased to see photographs of their work displayed on the Transum website and have sent some more exclusive puzzles. We are no closer to solving the level 8 puzzle though. The only clue was “you all should think a bit differently”!

Don’t forget that October is the spooky, scary month leading up to Halloween. Get into the spirit (pun intended) with some of the Halloween activities that can be found on the website. You could start with Trick or Treat.

If you are still reading you must be a loyal Transum fan. I wonder if you could help by replying to this email with one word (or phrase). What do you use the Transum website for most often? Which section (games, Starters, puzzles, exam-style questions, Random Name Generator etc.) should I spend my time improving to better support your teaching?

Finally the answer to the puzzle of the month can be worked out as follows:

If the mode is two and the median is six then the numbers can be represented as 2, 2, 6, x, y where x and y are yet to be found.

If the mean of the five numbers is 5, then the sum of the five numbers must be 25.

2 + 2 + 6 + x + y = 25

Then x+ y = 15

x and y must both be greater than 6 and they must also be different integers. It therefore follows that x = 7 and y = 8.

The five house numbers are 2,2,6,7 and 8.

That’s all for this month,

John

P.S. Why did the mathematician think that Halloween was the same as Christmas? Because 31 OCT = 25 DEC.

# February 2016 News

Hello, I hope you are fit and well and ready straight away for February’s puzzle. It’s a story to make you think, calculate and wonder. Apologies to those who have been using the Starter of the Day regularly as they’ll probably have come across this puzzle before. It’s the Starter for 19th June.

Here’s the story: Three people enjoy a meal at a restaurant. The waiter brings the bill for £30 so each person pays £10. Later the chef realises that the bill should have only been £25 so he sends the waiter back to the table with £5. The waiter was not very good at Maths and could not figure out how to divide the £5 so he gave each person a £1 and kept £2 for himself.

So….the three people have paid £9 each for the meal and three times £9 is £27

The waiter kept £2 so £27 + £2 = £29

What happened to the other pound?

Well that’s given you something to think about. The answer will be at the bottom of this newsletter.

January has been another busy month at Tran Towers and a number of activities have been added or updated. Here are the notable items.

Equivalent Fractions is the very latest self-marking exercise which was only added on the last day of January but already eight virtual trophies have been awarded to people completing it. The first two levels are basic colouring-in tasks. These very visual activities help pupils understand why certain fractions can be described as equivalent using diagrams of fraction walls and pizza sector slices. Level 3 is a more traditional exercise in which pupils have to fill in the missing number in pairs of equivalent fractions.

The 27th January Starter of the Day is a twenty-question mental arithmetic test. It has been updated to allow teachers to vary the speed of the test and edit the questions to better suit their pupils. It’s the sort of Starter you could bookmark to use regularly when the time comes for a light-hearted quiz on a particular topic.

The Pairs games have always been very popular. They add variety to a Maths lesson and can be played by one or two pupils sharing a computer. The latest one to be added is called Fraction Percentage Pairs and, as the title suggests, challenges pupils to match common fractions with their equivalent percentages. The pairs games also come with drag-and-drop warm up activities and multiple choice quizzes using the same cards used by the pairs game.

Factor trees is another self-checking exercise which helps student learn how to find the prime factors of numbers. The branches of the trees grow according to which factor pairs the pupil has chosen for each stage of the factor tree.

Next time you are teaching Venn Diagrams book the school hall or playground to do the Human Venn Diagrams exercise. Surely the learning must be all the more effective if you are part of the giant Venn diagram? This activity is part of the Transum People Maths collection.

Finally a randomly-generated Travel Graphs series of exercises has been added to cover distance-time and speed-time graphs.

The answer to this month’s puzzle is quite simple. The final paragraph of the story should read: The waiter kept £2 and £27 − £2 = £25, the correct cost of the meal!

Here is a similar puzzle from Thailand: “You borrow money from your Dad (500 baht) and your Mom (500 baht) to buy a phone that costs 970 baht. You then you have 30 baht change from the shop so you return 10 baht to Dad and 10 baht to Mom and you keep 10 baht yourself. But 490 + 490 = 980 and the 10 baht that you keep totals 990 baht. Where is the missing 10 baht?”

Have a good month

John

ps I will do algebra, I’ll do trigonometry and I’ll even do statistics but geometry and graphing is where I draw the line!