Hello, and welcome to the forty first Transum newsletter which is for the month of April 2018. What a pity April Fool’s Day falls on a Sunday this year. You won’t be able to catch your pupils out with the 1st April Starter!

First on the agenda is the puzzle of the month.

Aynuk and Ayli needed to cut the grass of their square lawn. They agreed that each person should cut half of the area of the square. Aynuk went first and cut a one metre wide border all the way around the lawn. Ayli then cuts the rest of the grass. What was the length of the sides of the lawn?

While you think about that (the answer is at the end of this newsletter) here are the most significant activities that have been added to the Transum website this last month.

Pie Charts. Pupils can practise the skills to construct and interpret pie charts using this self-marking set of exercises. Don’t forget that you, as a subscriber, can keep track of the trophies earned by your pupils in the Class Admin section of the website.

The world’s most accurate pie chart showing the amount of pie still to be eaten!

Pie Chart Creator. This is a quick and convenient tool for rapidly creating simple pie charts. It came about as a result of me needing to create pie charts for the activity mentioned above. It doesn’t have lots of features but its strength is its ease of use for fast results.

Pick up Sticks. If you were to pick up the sticks from the pile (randomly generated when the page loads) so that you were always removing the top stick what calculation would you create? What would be the answer to that calculation? This can be used as part of your BIDMAS (PEMDAS) revision repertoire.

Snow days Maths. Some mathematical activities to keep pupils’ brains active and continue their learning while school is closed due to bad weather (or any other reason). Links are provided towards the bottom of the page which you can send to your pupils so they can access the particular activity set you have chosen.

Emergency Maths lessons. An ever-growing collection of mathematics lesson plans to be used on the rare occasions when a class is left without their normal teacher and you are stepping in at very short notice. I’m guessing most people won’t use them in full but cherry pick the good ideas!

Online Logo Levels 2 and 3. What is now level 1 of online logo has been an extremely popular part of the Transum website for some time. The two new levels use a more sophisticated version of the Logo programming language with many more commands available. The challenges in Level 2 include using bearings to guide the turtle and Level 3 introduces procedures.

Graph Equation Pairs. A collection of activities and games involving matching the equation with the image of its graph. The graphs include quadratics, cubics, reciprocals, exponential and the sine function. Good for a lesson Starter or Finisher.

Simultaneous Solutions. Arrange the given pairs of simultaneous equations in groups to show whether they have no solution, one solution or infinite solutions.

Ratio Clues. Arrange the ratio clues in the clouds in a logical order to work out the values of the twelve letters. Involves simplifying ratios and recognising equivalent ratios.

Last month I told you about the new activity called Olympic Rings. There are three levels each with a different ring total. These are 11, 13 and 14. One teacher asked why there was not a level based on a ring total of 12. Apparently it can’t be done but how do you prove it?

I had a go at proving it but got stuck. I even resorted to posing the question on Reddit and although a computer programmer proved it using a brute force (the exhaustion method), I am sure there must be a short, elegant proof out there somewhere. So if you can prove the ring total cannot be 12 please share your proof.

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. Fingers crossed that there are no hosting issues in the pipeline.

Newsletter puzzle answer: Let the sides of the inner square that Ayli cuts be x metres long. The sides of the square of the whole lawn will therefore be x+2 metres long.

As the whole lawn has twice the area of the inner square the following equation can be constructed:

2x^{2} = (x+2)^{2}

2x^{2} = x^{2} + 4x + 4

x^{2} – 4x – 4 = 0

This can be solved using the quadratic formula and the positive solution gives the practical value of x

The answer (length of the sides of the lawn) is 6.83m (to 3 sf)

That’s all for now. Have a good April

P.S. There’s a fine line between numerator and denominator!