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Coaches to Cambridge

Tuesday 1st October 2019

It's October already; the month that begins with the ‘oct’ prefix but is the tenth month of the year (do you know the reason for that? – clue: think old calendars). I will begin the month, as usual, with a puzzle.

I travelled by train when I visited Cambridge this summer. The train had nine coaches labelled A (at the front) to I (at the back). Can you figure out which coach I was in if the product of the number of coaches in front and behind me is three less than it would have been if I were three coaches closer to the back of the train?

Train Sum

Incidentally while I was in Cambridge I visited the Whipple Museum of the History of Science and took some photographs of their calculator collection which I've posted on the Calculator topic page.

My next job is to tell you of the resources I have added to the Transum website during the last month.

The HCF and LCM Calculator could be used to find the highest common factor and lowest common multiple of two numbers but it also shows, in an variable-speed animated way, how the Indian Method is so efficient and useful. Of course pupils will need to be able to find common factors which brings me on to the next activity.

New Maths Learning Resource

My list of Divisibility Tests has been updated with a surprising new addition. The divisibility test for 7 is thanks to a 12-year old pupil, Chika Ofili, from Westminster School.

In a bored moment, Chika had turned his mind to finding a divisibility test for seven and this is what he came up with. He realised that if you take the last digit of any whole number, multiply it by 5 and then add this to the remaining part of the number, you will get a new number. And it turns out that if this new number is divisible by 7, then the original number is divisible by 7. What an easy test!

For example, take the number 532

53 + 2 x 5 = 63

63 is a multiple of 7, so 532 is divisible by 7

Well done Chika!

New Maths Learning Resource

The new Histograms exercises include questions in which you can drag bars to their correct heights as well as more traditional type questions. The higher levels require an understanding of frequency density and how it can be used to calculate the areas of the bars.

New Maths Learning Resource

I am developing a set of exercises called Numbasics with a particular student in mind. She is in Year 6 but working above expectations. The plan is for her to work through one of the levels each week. Each level contains 24 key skills and mental strategies questions and, on completion of the exercise, produces a list of the mistakes in a printable format for her to discuss with me and to work on before retaking the level (questions numbers change on each attempt) next week. If she gets all 24 questions correct her time is recorded and the following week she would work on the next level.

New Maths Learning Resource

I'll be adding new levels to Numbasics as the Term progresses.

For the first time I have acquired an original game from a programmer based in New Zealand. The game is called Alpha Twist and as well as being fun and challenging gives learners a 'feel' for the effects of rotation. A great way to introduce or extend the study of transformations. [At the time of writing it does not yet run on Apple devices]

New Maths Learning Resource

For many older students taking an IB Maths course the TI-Nspire is the calculator of choice. I have come up with 20 Essential Skills that students should have and I have produced a PowerPoint presentation demonstrating these skills. It's the sort of visual aid a Tutor might find useful as one skill per week can be learnt/revised then practised following the instructions in the presentation.

This month I would like to welcome new or returning subscribers from United Kingdom, United States, Australia, New Zealand, Germany, Spain, Belgium, Ireland, Canada and Korea.

Having spent almost half of my teaching career at a big International school working with Maths teachers from around the globe my ears would twitch each time I heard the subject being referred to as Math rather than Maths. Even some of my English colleagues started dropping the s.

I always assumed that the word maths was the correct abbreviation of the word mathematics but yesterday my confidence was shaken. There is an argument that the word math is a more logical nickname as explained on the Grammar Girl podcast. You can hear the audio excerpt on the Math vs Maths Pairs Game page and make your own mind up.

New Maths Learning Resource

Finally the answer to this month's puzzle:

Let’s assume I was in coach that was n from the front of the train.

(n – 1)(9 – n) = ((n+3) – 1)(9 – (n+3)) - 3

(n – 1)(9 – n) = (n + 2)(6 – n) - 3

9n – n2 – 9 + n = 6n – n2 + 12 – 2n – 3

10n – 9 = 4n + 9

6n = 18

n = 3

So I was in coach C

That's all for now,

John

PS. Why do mathematicians think that Halloween is exactly the same as Christmas?

Because 31 Oct = 25 Dec. (31 in base 8 is equal to 25 in base 10 or 3x8+1 = 2x10+5)


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