9 Trafalgar Square Puzzles – One unsolved

You have just begun reading the Transum Newsletter for September 2018 and, as usual, it begins with a puzzle for the month.

My clock does not have any numbers on its face, just markers for each hour/five-minute interval. I looked at it in a mirror one morning and noted the time it appeared to be showing. An hour and a half later while eating breakfast in the kitchen I noticed the clock on my phone is showing the time the reflected clock appeared to show earlier.

Assuming that both clock and phone were showing the accurate time, what time was it when I first viewed my clock in the mirror? The answer is at the end of this newsletter.

The majority of Transum subscribers live in the northern hemisphere so a Back To School theme is appropriate. There are many ideas and resources on the Transum page created for this time of year. Please let me know if you have any other suggestions for teachers meeting classes for the first time.

I stayed in London for a while during the summer and was delighted to see that a pavement artist in Trafalgar Square had drawn a set of maths puzzles instead of the usual art seen in the area. I photographed the puzzles and created an interactive version which are now online. Each puzzle is in the form of a three by three square containing numbers linked by hidden rules. I have named this kind of puzzle as a Trafalgar Square! (Can you see what I did there?)

Thanks to help from some clever people who have seen my photographs online already I have figured out the answers to all but one of the puzzles drawn in chalk by the artist from Slovakia. If you can help solve the puzzle marked Level 8 I will be eternally grateful.

Another new addition to the website is called Vector Cops. Teachers of an older persuasion may recognise the idea from a program popular in schools in the 1980s called Vectmeet, originally published by SMILE (Secondary Mathematics Individualised Learning Experiment). I have created ten levels of difficulty hoping to achieve a low threshold and a high ceiling.

I have just put the finishing touches to a new Advanced Starter called Test Scores. It is designed to question the misconception that when adding fractions you add both the numerators and the denominators. I hope you get a good reaction from your students who think they have a sound understanding of fraction arithmetic.

The final new addition to the website which appeared last month is called Rough Answers. It is a set of exercises on rounding values in a calculation to find an approximate estimate of the answer. Click on the Description tab to find a link to a Fermi problem about piano tuners. As a Transum Subscriber you have access to a link to a video about Fermi problems and how to solve them. The link is at the bottom of the Fermi Problem page if you are signed in.

I am currently in Bangkok, Thailand where the vast majority of cars have tinted windows so dark that you cannot see anything inside the car. My car does not. Yesterday afternoon I parked my car in the car park next to the Sky Train station and as I got out of the driver’s door I noticed my reflection (these tinted windows act like mirrors) in the window of the car next to mine. I saw that my collar was half up so I straightened it. I also gave my hair a flick then got really close to the window to check I had no vegetation caught between my teeth. Just as I had contorted my face to see clearly my left back molars the engine of the car started and the car pulled away. I felt slightly embarrassed to be honest!

That true story from yesterday is a convoluted way of changing the subject to mirrors and the answer to this month’s puzzle. The time I looked at the clock in the mirror it was 5:15am but appeared to be 6:45am.

That’s all for this edition of the newsletter, I plan to read the new book by Hannah Fry this month called Hello World.

Happy New (School) Year,

John

PS. Maths teachers are very good dancers because they have many algorithms

September 2014 News

This is the September 2014 Transum Newsletter bringing you the latest news from Transum Mathematics. If you are in the UK or US it is ‘Back To School’ time while the rest of you it is ‘Business as Usual’.

Talking of ‘Back To School’ it is the time teachers meet classes for the first time often with little or no information about the abilities and personalities of the pupils in front of them. There are some great starter ideas that work well with pupils of all abilities and quickly give you, the teacher, a very good idea of the mathematics they can remember. In particular BTS (Back To School) encourages pupils to write down equations of their own devising. A quick walk around the classroom while they are doing this activity will provide you with a wealth of information about how sophisticated their understanding of the subject is. You’ll spot the pupils struggling to come up with even the most basic expression while the bright sparks will stand out with their ability to produce a great variety of equations involving not just the run-of-the-mill concepts.

Did You Know?

There are mirror sites for Transum containing all of the starters and activities but stored on different servers. As well as Transum.org there is Transum.com and Transum.info (Transum.net is currently working too but is soon to be discontinued). The mirror sites provide you with reassurance that should Transum.org go offline (it does happen from time to time) you can quickly switch to a mirror site to find the activity you need for your lesson.

Unfortunately your Transum account (and pupil trophies) only operate on Transum.org so this is not a perfect solution but it’s better than nothing right? Fingers are crossed that the server does not go down during the busy month of September. Our web hosts (called GoDaddy) have had a very good up-time record so far.

Connect 4 Factors is a game, created at the beginning of August, which uses the ‘four in a line’ principle of the popular Connect 4 game but each of the counters contains a number and the twist is that four in a line means four numbers with a common factor (except one).
I have seen too many students that, while understanding the algebraic concept of factorisation, can not easily spot the common numerical factors. Hopefully this game might help improve common factor spotting ability. Games are such a nice change from exercises for practising mathematical techniques!

Chess has been added to the Strategy Games section. The interactive chess games comes with some mathematical puzzles that might interest your pupils. There’s a Draughts game there too.

Circle Theorems are essential learning for pupils in upper Secondary and we have put together some big, bold diagrams of each of the important ones to support your teaching. The diagrams are accompanied by dynamic models powered by GeoGebra and Autograph.

Numerology is the final new activity for August. It’s modestly hiding on the Fun Maths page as we are not really sure how teachers will decide to use it. It is still not in its final format but is fully working for testing. It is designed to inform pupils that the early mathematicians had some strange ideas about the mystic properties of numbers. It is also designed to make the notion of fortune telling questionable buy making the process transparent and a little ridiculous. The activity saves it self in the end however with some questions about the mode, mean and range of the pupil generated data. For the time being it can stay in ‘Fun Maths’!

National Curriculum

Those of you in the UK might be embarking on a brand new scheme of work this term due to the new National Curriculum. Transum has a page of suggested activities for each curriculum statement. Click on the strands and statements  on our National Curriculum page to drill down to the activities.

Subscribers

Welcome to new subscribers from the UK, US, Australia, New Zealand and, for the first time, Guatemala. You are all very welcome.

Thanks to those of you who leave comments on the activities. It is really good to get your feedback. Positive comments provide a warm, satisfied feeling while suggestions for improvement often lead to an activity being redesigned.

Have a good September!

John

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