Tag Archives: Probability

7 great Maths games to play instead of doing traditional exercises.
















That’s all for this month,



7 New Resources for the Maths Classroom




  1. First Impressions


  1. Weekly Workout


  1. Brainbox


  1. Plinko Probability


  1. Trigonometry Advanced


  1. Triangle Solver





  1. ChristMaths Activities


The answer to this month’s puzzle is:

  • The nine two digit numbers that end in a zero;
  • The nine two digit numbers that end in a one;
  • The nine two digit numbers that end in a five;
  • The nine two digit numbers that end in a six;

These added together give a total of 36.

Enjoy the Christmas holiday and enjoy the ChristMaths activities,


P.S. Calendars, their days are numbered.

November 2016 News

Welcome to yet another newsletter from Transum Mathematics. As has become traditional I will start off with the monthly puzzle.

Trains from Punspace station go either north or south. Those going north leave hourly, those going south leave hourly. If I arrive at the station at a random time the probability that the next train to leave will be going north is five times the probability that the next train to leave will be going south. How could that be?

While you are thinking about that here is some news about the latest additions to Transum Mathematics.


Kite Maths is a very visual, practical colourful activity leading to the discovery of important geometrical theorems. A new page of interactive animations created in Geogebra has now been added. These dynamic images are great visual aids for classroom use.

Some excellent interactive activities have been created by an organisation called PhET (Physics Educational Technology) and the mathematical simulations are being added to the Transum website. Founded in 2002 by Nobel Laureate Carl Wieman, the PhET Interactive Simulations project at the University of Colorado Boulder create these appealing Maths and Science simulations. They are based on extensive education research and engage students through an intuitive, game-like environment where students learn through exploration and discovery.

During October the following PhET activities have been added: Area Builder, Grid Arithmetic, Fraction Matcher, and Function Builder. You can find them by searching for activity title using the Transum search box (in the footer of every page) or by looking them up on the relevant topic page.

The activity called Clouds was updated last month. It has now been split into five levels and the higher levels include decimals and fractions. The idea of this activity is that clouds have magically floated across some calculations obscuring one of the numbers. Pupils need to find a strategy for working out what is behind each of the clouds. Teachers will see the link with algebra, rearranging formulae or solving equations.

The Mixed Numbers exercise has also been update. Level 5 now includes a variety of questions with words and diagrams! You as the teacher can decide whether pupils should be using this exercise to practice their pen and paper techniques or use it as a calculator exercise, making sense of the calculator’s strange fraction notation.

Coming very soon (hopefully by the end of this week) are some GCSE(9-1) practice papers for pupils on a Foundation level course. Each Weekly Workout contains 7 exam-style questions. The first six can be answered online but the seventh requires the student to draw something that needs the teacher to check.

The answer to this month’s puzzle is best understood by considering what the timetable for departures might look like. If the northbound trains leave at 10 minutes past the hour and the southbound trains leave at 20 minutes past the hour then there’s only a ten minute window for you to arrive at the station for the next train to be going south. There is however a fifty minute window for arriving to find the next train is northbound. Hence the probability that the next train to leave will be going north is five times the probability that the next train to leave will be going south.

Enjoy November


P.S. I don’t understand how to double 2n. It sounds 4n to me.

April 2016 News




The answer can be found at the end of this newsletter.










Enjoy the month of April.



September 2015 News

It seems such a long time since the last newsletter but here it is again to welcome the month of September 2015. I have had a wonderful summer (northern hemisphere) and managed to visit lots of places and catch up with many old friends. I always had my laptop with me so found the time to write more puzzles, quizzes and activities to add to the ever-growing Transum collection.

Before going any further let’s go straight to the puzzle for this week. This is to give you something to think about as you commute, exercise or relax today so don’t look at the answer at the bottom of this newsletter if you want to enjoy the challenge.

Three very logical mathematicians walk into a bar (change this to a sweet shop if you are telling it to your pupils). The barman asks if they all wanted a drink. The first mathematician said “I don’t know”, the second mathematician said “I don’t know” but the third mathematician said “Yes we do”. Can you explain how the third mathematician could be so certain?

While you think about that here’s a mention of some of the new activities created since the last newsletter.

The Fractal Mosaic is an interactive, animated version if the Snowflake Squares activity. A fractal-like pattern can be created by following a very simple set of instructions that are repeated a number of times. The end result makes excellent display material. Talking of which, a new section called Maths On Display has been created giving you some ideas of how your pupils can engage in mathematical activities that produce very pleasing results.

Fractal Mosaic

Follow the rule repeatedly to create this beautiful pattern

Following the success of the Bridge Crossing starter a challenge called ‘Without Lifting the Pencil’ provides pupils with six designs that they have to decide whether they can trace according to the rules. Instead of actually using a pencil and paper the Transum interactive version allows them to click dots (the nodes) to simulate the tracing and makes it easier for them to try many different routes quickly and not worry about making mistakes.

A Frequently Asked Questions section has been added for subscribers but, thus far, there are not many questions and answers posted. The plan is to add to this slowly but surely over the coming months. If you have any questions about using Transum Mathematics please let me know as your question might be suitable for this FAQ page.

The One Torch Tunnel challenge has been added as an interactive page which I hope will be as popular as River Crossings is. It is quite easy to get all four people through the tunnel but not so easy to do it in the optimal time.

A Fibonacci Quest section has been added. The plan is to, over a period of time, add fascinating Fibonacci facts to these pages but each new page will have an interactive aspect to it so that pupils learn by doing!

The Probability Washing Line is certainly not a new idea. Pupils are invited to hang out the shirts, each containing a probability word, on a line stretching from impossible to certain. The software will check their attempts according to some very loose rules.

There was nothing on the website to practise Telling the Time … but now there is! Lots of analogue clocks with some mixed questions thrown into level four. As with all other activities on the site let me know if you think this section should be expanded.

The answer to the puzzle asked at the beginning of this newsletter can be explained as follows.

If the first mathematician did not want a drink he would be certain that not all three wanted a drink as there was at least one of them (himself) that did not. He would have therefore replied “No” instead of “I don’t know”. The third mathematician was therefore sure that the first mathematician did want a drink due to his answer.

The same argument can be also applied to the second mathematician who must also have wanted a drink.

The third mathematician was quite certain he wanted a drink himself bringing the total to three.

That’s all for now. Enjoy September and if it’s the beginning of your school year enjoy all that newness and new-beginning enthusiasm that’s around at the moment.


ps How many times can you subtract 7 from 83, and what is left afterwards?


June 2015 News

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

The puzzle for this month is about a game in which a coin is tossed repeatedly. If it comes up heads Pascal gets a point but if it comes up tails Fermat wins a point. The first person to win three points is the winner and receives the prize of £12.

Unfortunately the game had to end abruptly after three tosses of the coin. Pascal had two points and Fermat had one point. They decided to share the £12 in a ratio that matched the probability of them winning the game if it had continued. How should they divide the £12?

That should give you something to mull over as you go about your activities today. It is worth noting however that if you think the answer is £8 and £4 you may have some more thinking to do. The answer is at the end of the newsletter but don’t look if you want to figure it out for yourself.

Hundreds of virtual Transum Trophies are earned by pupils around the world each day for completing a Transum online activity. The trophies are collected in their own virtual trophy cabinet online which the pupils can proudly show to their teacher, parents or friends.

As a Transum subscriber you can award Teacher Trophies to your pupils for all sorts of achievements. You could issue a trophy for a good effort, taking part in a group project or any reason you see fit. Each pupil can receive a maximum of one Transum Teacher Trophy each day.

The button linking to the trophy awarding page is on your ‘My Account’ page.


As usual there have been a number of additions to Transum Mathematics last month and here is a roundup of those worth mentioning.

For those of you involved with teaching Formal Written Methods there are some examples of standard ways to set out the calculations along with buttons linking to online exercises providing some practice.

Five related activities are provided to support your teaching of correlation. The starting point would be Cartoon Scatter Graph  which is a very visual way to convey the concept of the scatter graph. Pupils have to place cartoon characters on a set of axes to show their heights and ages.

To introduce the concept of correlation there is nothing more memorable than being a part of the graph yourself so Human Scatter Graphs is a highly recommended next step. This resource provides pairs of variables, each relating to the pupils, and asks them to find their position in the room relative to a set of very large axes.

Next is a sorting activity called Correlation which consolidates the understanding of different types of correlation.

The basics are covered by Plotting Scatter Graphs which ensures that the pupils practise the manual point plotting skills before they learn to leave the hard work to the calculator when answering Exam-Style Questions.

Now special awareness skills are a funny old phenomenon. Some children find activities so easy while others struggle, and it is not always the best mathematicians that do well. To provide practice there are a number a different ways you can approach this. Try Net or Not and Plans and Elevations. There is no substitute for making models and setting up situations in the classroom to really get to the bottom of this topic though.

The most popular online exercises, if the number of trophies earned is the defining criteria, are the basic arithmetic quizzes. A new basic exercise called Powten has now been added which has a number of levels, containing twelve questions each, requiring an understating of the easy methods of multiplying and dividing by powers of ten.

Thanks to everyone who have ever given a Starter a score. If you click on the stars on a Starter page you can see a bar chart showing the distribution of the votes. Currently the most popular starter of the year is How Many Triangles and the least popular is Chin Ups. I wonder why!

Finally the answer to the puzzle posed at the beginning of this newsletter. Consider the following equally likely scenarios for the outcome of the next two tosses:

  • Heads heads
  • Heads tails
  • Tails heads
  • Tails tails.

Three of the four possibilities would make Pascal the winner so the prize should be shared in the ratio 3:1 meaning that Pascal should receive £9 and Fermat should receive £3.

Not many people get the right answer first time! This puzzle is just one of the Advanced Starters designed for older students.

That’s all


Ps. What did the mathematical acorn say when it grew up?

A. Gee I’m a tree (Geometry).

April 2015 News




Best Dice

Best Dice

  • The red dice has threes on all of its faces.
  • The blue dice has four fours and two zeros.
  • The yellow dice has three fives and three ones.
  • The green dice has four twos and two sevens.












… A high-pot-in-use!

March 2015 News












ps 3.14% of Sailors are PI rates!