Tag Archives: Divisibility

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.

Calculator Keys

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


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

Delightfully Divisible

Best wishes for August wherever you may be. I am in the UK and am about to catch a train for Glasgow, a city I’ll be visiting for the first time. The record heat wave in the UK has come to an end and today water is falling from the clouds. I think it is called rain but it has been so long since I saw it that I can’t be sure. Let’s start with a rainy-day puzzle:


Three thousand eight hundred and sixteen is delightfully divisible. The first digit is, of course, divisible by one. The number formed by the first two digits, 38, is divisible by two. The number formed by the first three digits, 381, is divisible by three and the number formed by the first four digits, 3816, is divisible by four.

Can you increase the list of digits to make a nine-digit number which is also delightfully divisible? Your answer should be a pandigital number containing all of the digits one to nine. The answer is at the end of this newsletter.

Talking of Pandigital Numbers, I have just uploaded a brand-new, two-level, self-marking quiz about them which touches on divisibility and, to a lesser extent, place value.

Other activities created in July are based on the ‘arranging the digits 1 to 9’ idea and provide a great environment in which to develop problem-solving strategies. For some the difficulty of the puzzle builds over a number of levels providing a low threshold, high ceiling learning activity. Try them for yourself and please let me have any feedback. They are Multitude, Double Treble and Triside Totals.

Sixteen other Transum activities were updated during last month as part of the Forth Bridge style cycle of keeping all of the content on the website fresh, easy to access and relevant to mathematics learning today. I am always happy to receive comments and suggestions and particularly ideas for new content.

You have probably heard the debate about summer learning loss. Research indicates that by the end of the long summer holidays, pupils perform on average, one month behind where they left off in the spring. It’s not too late to send an email to your pupils with suggestions of Maths activities they can do during the down time. I have put together a list of easy-to-assign activities covering a wide range of topics on the Holiday Activities page. Please let me know if you have any other ideas.

Don’t forget that if ever Transum.org goes offline you can always find the activity you need on one of the mirror sites: Transum.com and Transum.info.

The answer to this month’s puzzle is 381,654,729. Did you enjoy working it out? Would it be a worthwhile challenge for your pupils? Go to the Delightfully Divisible page for an interactive workspace and a link to a list of divisibility tests. Depending on your pupil’s abilities (and the time of day) you may decide to give them a clue as I did to you.

That’s all for now, enjoy the month of August,


P.S. Why is a dog with a bad foot like adding 6 and 7?

A. Because he puts down three and carries the one.

July 2016 News

Before reading the rest of this newsletter you are challenged to find five two digit numbers that are multiples of three. The ten digits used in your five numbers must all be different!

Well that’s the puzzle for this month. The answer will be at the end of this newsletter.


More brand new activities have been added to the Transum website during the last month; the very latest of which has only just been uploaded. It is called Bidmaze and is a numeracy challenge requiring guiding a token through different mazes picking up mathematical operations on the way. Successfully completing a stage requires that the order of operations produces the given target. There are ten stages in each level and three levels. Level 1 targets the four basic operations with positive numbers. Level 2 extends level 1 to include negative numbers and level 3 includes finding squares and square roots. It is quite addictive!

Snooker Angles is a game for one or two players or teams. It involves the ability to estimate the angle (or bearing) of the direction the ball should travel to go into any one of the six pockets around the border of the snooker table.

Where’s Wallaby is an activity for pupils involving coordinates and, for those who have learned it, Pythagoras’ theorem. Choosing coordinates on a grid will reveal the distance away that a hiding wallaby is lurking. Pupils will find themselves considering the loci of all possible hiding places before making their next guess. Transum subscribers have access to the settings to change the way the clues are given and how many wallabies must be found before a trophy is awarded.

23 or Bust is a favourite game I have played with classes I have taught over the years. This new interactive version of the game is designed for two players or one player against the computer. By playing the game a number of times pupils will start to realise that there is a strategy to be revealed. An optional printable worksheet is provided to help pupils understand the strategy.

Counter couldn’t be simpler. The title says it all, it counts! This resource can be found in the Shine+Write collection and is designed for teachers to project in the classroom for a number of learning experiences.

Finally Standard Order provides a drag-and-drop list of numbers in standard form for pupils to sort. Another example of an interactive task that can’t be provided in a hard-copy textbook.

For future reference there are two ‘mirror’ sites that contain all the Transum Starters and activities. They are at www.transum.com and www.transum.info The only difference is that they don’t contain the details of your Transum subscription account so you won’t be able to log in there. If it looks like Transum.org will be offline for a long time then I will transfer the database containing your details to Transum.com so you will eventually be able to log in there too.

There are many correct solutions to this month’s puzzle but here is one: 12, 36, 45, 78 and 90.

Did you know there is a trick for quickly determining if a number is divisible by three? You can find it with similar tests for divisibility on the Divisibility Tests page.

You can find more challenges similar to this month’s puzzle, ready made to project for your Maths class, on the Hot Numbers Challenges page.

That’s all for this newsletter


P.S. There are three types of people in the world, those who can count and those who can’t.