# June 2016 News

This month’s puzzle is all about numbers when written as words.  Take the smallest positive whole number containing the letter ‘a’ away from the smallest positive whole number containing all of the vowels.

Add to this total the number that has the same number of letters as its value and then add the largest number that has only one syllable.

Divide this total by the number which has all of its letters in alphabetical order.

That should keep you busy if you resist the temptation to peep at the answer at the end of this newsletter!

May was another busy month adding and improving content on the Transum Mathematics website. Here are the highlights:

The BIDMAS logo has been redesigned to show that division does not always come before multiplication as those two operations should be evaluated from left to right. The same is true for addition and subtraction. What do you think?

Investigating the properties of algebraic graphs has been transformed over the last ten years with the widespread use of graphic display calculators and graph plotting software on computers and mobile devices. On Transum you can now access the wonderful Desmos on the new Graph Plotter page. The suggested investigations are in draft form at the time of writing but will be developed further during this month.

In addition to the Graph Plotter is a Graph Patterns exercise which allows pupils to earn trophies for recognising the graphs and correctly finding their equations. There are currently two levels containing linear (level 1) and quadratic (level 2) graphs.

A new Collecting Like Terms exercise has been added with links to exercises on using brackets and expanding products of two binomials.

For older students in the middle of exam revision there is a new page containing a growing list of objective checklists for various common Maths exams. The checklists are presented in an interactive format which allows students to go through each objective and classify it as easy, OK or help!

The Areas Investigation and How Many Squares (2) pages now have camera icons appear each time a shape is completed. This interface allows pupils to find shapes and then drag the ‘photos’ they have taken into some kind of order to help spot missing shapes.

Subscribers have access to the Worksheet section of the website and a printable page for teachers has just been added. It is a very simple idea but something you may find useful. When you have finished marking a lot of test papers it speeds up the task of converting a lot of test scores to percentages. It is called Test Scores To Percentages.

This idea will only save you a small amount of time compared with using a calculator or a spreadsheet but every second counts when you have a pile of marking in front of you. I personally have found it useful for speeding up the conversion and rounding of percentages for many years of test marking. You could also put tally marks next to the scores to get a quick picture of the spread of the marks.

Finally here is the answer to this month’s puzzle:

• The smallest positive whole number containing the letter ‘a’ is 101.
• The smallest positive whole number containing all of the vowels is 1005.
• The number that has the same number of letters as its value is 4.
• The largest number that has only one syllable is 12.
• The number which has all of its letters in alphabetical order is 40.

The calculation is (1005 – 101 + 4 + 12) ÷ 40

That’s all for this month,

John

P.S. If the test question is three minus the square root of nine you can write down nothing but get full marks!

# May 2016 News

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 16ᵒ, 64ᵒ and 100ᵒ. The angles of the quadrilateral could be 16ᵒ, 100ᵒ, 100ᵒ and 144ᵒ but if the quadrilateral was a symmetric trapezium they could be 36ᵒ, 36ᵒ, 100ᵒ and 100ᵒ. This puzzle is in fact the Starter for April 7th.

That’s all for now,

John

p.s. Try to avoid doing calculus when you are thirsty. You have heard the warning, don’t drink and derive!