I hope you enjoy reading this, the September 2017 edition of the Transum Newsletter. It begins with the puzzle of the month.

How many different ways are there of arranging the digits one to four to make a four digit number? That’s a familiar question in the Maths classroom. This month’s puzzle is to find the sum of all those four digit numbers in a concise, efficient and elegant way. The answer can be found at the end of this newsletter.

For those in the northern hemisphere it’s Back To School time and the Transum website has a list of resources you may find useful at this time of year. Please let me know if you have any suggestions to further develop that area of the website.

The months of July and August have been busy with the Transum laptop being heavily used to create new Maths learning materials for you to use in the classroom. Here are some highlights:

Area Maze is the Transum classroom version of Menseki Meiro, the creation of Naoki Inaba, a prolific inventor of logic puzzles. He came up with the idea after being asked to come up with a puzzle by the head of a school in Japan. Have a look and let me know if I should come up with more levels of difficulty.

Fraction Dissect is an interactive activity. By drawing a straight line between the dots can you split the rectangle to give the target fraction. I was using it this week with pupils of different ages and they all found it a worthwhile learning experience.

The game Skunk is quite new to me but apparently teachers have been playing it in the Maths classroom for years. It gives pupils a feel for probability and generates discussion about the choices made while playing the game. This new Transum version of the game makes life easy for the teacher by providing the dice and results chart.

Numbers in Words is an old Starter but I have updated it as the date, 19^{th} September, I found out is Talk Like A Pirate Day. I couldn’t resist giving it a pirate theme.

The Shine+Write collection has two new resources. Compound Interest calculator and Normal Distribution calculator allow you to make up problems and quickly find the solutions as pupils develop their own calculator skills. While on the subject the Calculator Workout page now has a new ‘skin’ option to accommodate those with Casio fx350es plus, fx83 and fx85GT plus calculators. I am still trying to find data on the types of calculators most popular in schools at the moment. Let me know if you have any information.

There was one National Curriculum statement that didn’t have a related Transum activity. That hole has now been filled by Estimating Powers and Roots which does what the title suggests. It is an animated interface in which pupils have to click on the integer which is closest to the root or power presented.

As part of a lesson introducing the use of the calculator’s degrees, minutes and seconds button to do time calculations I snipped a section of the London Underground map to produce the Walking Times quiz. Half the fun is finding the stations on the map!

The Exam Questions database is now being added to at a rate of one new question each week. Each new question is adapted (inspired by) one of the questions from the recent GCSE papers and a full worked solution is provided. Hopefully this resource will support the cohort that will be taking this exam next year which includes my nephew, Ben. Fingers crossed.

Here is the answer to this month’s puzzle. There are 24 different ways to make a four digit number from the digits one to four. This first few are shown here:

1234

1243

1324

1342

1423

1432

2134

2143

…

It can be seen that each digit appears in each place-value column six times. The sum of the 24 four-digit numbers is therefore:

6 x 1 x (1000 + 100 + 10 + 1) +

6 x 2 x (1000 + 100 + 10 + 1) +

6 x 3 x (1000 + 100 + 10 + 1) +

6 x 4 x (1000 + 100 + 10 + 1) =

6 x 10 x 1111 = **66660**

This method of finding the solution can be extended for situations involving five or more digits.

That’s all for this month,

John

P.S. Did you know that three out of two people have trouble with fractions?