# 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

John

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

# October 2016 News

This is the Transum Newsletter for October 2016, the 10th month of the year. Have you ever noticed that the month name begins with the suffix ‘Oct-‘ suggesting eight and not ten. There is a reason for that and a quick internet search will reveal it to you.

Let’s begin with the puzzle for this month which is about three hungry children.

There was a short queue in the school canteen. Ayden was directly in front of Betsy who was directly in front of Carl.

Aden’s age is an even number but Carl’s is odd. Is a person with an even age directly in front of a person with an odd age? The answer is at the end of this newsletter.

I am very keen to tell you about some of the new additions to the Transum website that appeared last month. The first is Maths Mind Reader. Absolutely everyone I’ve used it with have been extremely impressed with this clever web page. As a Transum subscriber you will be see the mathematics that makes it work and Secondary pupils should be able to understand and even prove the concept.

A Transum website visitor, Les Page, sent me an addictive little puzzle he has devised called Zygo. He has kindly allowed a Transum interactive version to be created which is now ready to improve the numeracy and problem solving skills of your pupils. Thanks Les.

Pupils quickly learn to recognise and name regular polygons but the new activity called Polygon People may help younger pupils to name irregular polygons too. The activity has three levels and only accepts the correct spellings.

For the older pupils (14+) the Completing the Square and Proof of Circle Theorems activities should support those entered for the higher tier of the GCSE exams (or equivalent).

At times when I have not been creating new content for the website I have had a small amount of time to look at an updated app that I have downloaded to my iPhone. Photomath has been around for a couple of years but I’ve been very impressed with the recent improvements. You point your phone camera at an equation, and it will give you the answer and show you the working. I’m still amazed it can read my handwriting!

Photomath supports arithmetic, integers, fractions, decimal numbers, roots, algebraic expressions, linear equations and inequalities, quadratic equations and inequalities, absolute equations and inequalities, systems of equations, logarithms, trigonometry, exponential and logarithmic functions, derivatives and integrals.

My only reservation against using it with pupils is some of the phrases used to explain the stages of solving an equation. “Move constant to the right side and change its sign. Move variable to the left side and change its sign” is less helpful than the notion of doing the same thing to both sides in my opinion.

The answer to this month’s puzzle is yes. We don’t know Betsy’s age but we do know it is either even or odd. Let’s consider the two possibilities.

If Betsy’s age is odd then Ayden (even) is in front of Betsy (odd) and the answer is yes.

If Betsy’s age is even then Betsy (even) is in front of Carl (odd) and the answer is yes.

So regardless of Betsy’s age, the answer is always yes.

A similar problem was devised by Hector Levesque and it was included in Alex Bellos’ Guardian blog. Unbelievably 72 per cent of the 200,000 people who answered the question got it wrong.

That’s all for this month.

John

P.S. Why do mathematicians think that Halloween and Christmas are the same?

Because 31 OCT = 25 DEC (You need to know about the octal number system to understand this month’s joke 318 = 2510)