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A Square Triangle

Sunday 1st May 2016

Hello and welcome to the newsletter for May 2016 which begins with this month’s puzzle for your pondering pleasure!

A particular triangle is drawn such that each of its angles are square numbers. What are those angles?

Too easy? Well consider a quadrilateral having all four angles as square numbers. What would they be? The answer is at the end of this newsletter.

This month saw the OCR exam board produce more ‘Check In’ tests as free-to-download pdf files on its website. These ten-question tests are proving to be very useful with Year 9 and Year 10 pupils. Each topic in their new GCSE syllabus has been mapped to a Check In containing questions relating to the initial learning required. Questions 1-5 cover procedural calculations, Questions 6-8 assess the learner’s ability to reason and communicate mathematically and Questions 9-10 relate to problem solving tasks.

OCR also produced a delivery guide for Mensuration and it was rewarding to see that a number of the sections within the guide contained links to Transum activities.


As usual there have been lots of updates and new content added to the Transum website this last month. The most recent addition is Digital Darts. A soon as it went live a couple of days ago it received hundreds of views and people began collecting trophies for completing the activity or winning the game. It provides a suitably challenging mental exercise for more able pupils while those who cannot cope with the mental manipulation can practise their written methods of addition and subtraction. As a subscriber you have the option to change some of the features of the game to make it easier (or harder!).

Another game that provides practice in a format more motivating than a traditional exercise is the BIDMAS Game. Players are challenged to claim squares on a grid by making given totals with the numbers that are randomly generated by four dice. This could make an engaging last ten minutes of a Maths lesson activity with the teacher challenging the whole class working as a team.

A gap in the Transum offerings has been filled with a Gradient of a Line twelve-question exercise. The questions are diagrams from which the gradient can be calculated by counting squares and then dividing rise by run. This exercise provides a small part of a larger learning experience about straight line graphs.

Another pairs game has been added. This one requires players to match digital and analogue times. This is another game that might work well if played as a teacher versus the whole class challenge at the end of the lesson.

One of the podcasts I enjoy listening to is Futility Closet. In a recent episode (number 103) some little-known mathematical history was described. In 1897, confused physician Edward J. Goodwin submitted a bill to the Indiana General Assembly declaring that he had squared the circle, a mathematical feat that was known to be impossible. The podcast episode examines the Indiana pi bill, its colourful and eccentric sponsor, and its celebrated course through a bewildered legislature. It’s definitely worth a listen!

Finally the answer to this month’s puzzle. The angles of the triangle are 16?, 64? and 100?. The angles of the quadrilateral could be 16?, 100?, 100? and 144? but if the quadrilateral was a symmetric trapezium they could be 36?, 36?, 100? and 100?. This puzzle is in fact the Starter for April 7th.

That’s all for now,


P.S. Try to avoid doing calculus when you are thirsty. You have heard the warning, don't drink and derive!

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