Tag Archives: Vectors

Maths Advent Calendar

Glad tidings and welcome to the Transum Subscribers’ Newsletter for December 2018. I am writing it a few days early due to the fact that I’ll be enjoying a weekend break in the sun when I would have normally written this on the first of the month. Lucky me!

Let’s begin with a festive theme. Here is the puzzle of the month:

St Nicolas’ Yuletide Choir is rehearsing daily for the local school’s Christmas assembly. Each member of the choir has blonde hair or blue eyes; One quarter of the members with blonde hair do not have blue eyes and one third of the members with blue eyes have blonde hair.

What percentage of the choir members do not have blue eyes? The answer is at the end of this newsletter.

Maths Advent Calendar

As soon as November is over it is quite acceptable to have a festive theme to your Maths lessons. To support this you can, starting on the 1st December, open a door of the Maths Advent Calendar and for each of the days leading up to the 25th enjoy a seasonal activity (from the Christmaths collection), laugh at a cracker joke and solve a mathematical word puzzle. Transum subscribers are able to open doors before the corresponding dates by using the unlock button which can be found lower down the Advent Calendar page when you are signed in.

This last month I have been working enthusiastically improving and adding to the resources at Transum.org. I have just finished Parallel Vectors, yet another activity in the Vectors collection. It is a quick, drag and drop, challenge to match vector expressions with others that represent parallel vectors.

I then copied that activity format to produce Parallel Graphs requiring the rearrangement of equations into the y=mx+c format to find their gradients.

A new vector activity that will appeal to a wider range of pupils is called Vector Maze. Already many have earned Transum Trophies for completing it and the optional challenge is to find the shortest route from start to finish. Chick on the instructions tab to see the latest world record.

Convoluted is the name I plucked out of the air for another brand new activity providing practice recognising multiples. There are three levels with the first including multiples of 2 to 5 while the last level includes multiples up to 12. Pupils can time themselves completing a level and work to improve their personal bests.

Don’t forget there’s also an audio version of this newsletter in the form of a podcast. This month the podcast also includes an advert I heard on Heart Radio for Maths teachers which I quite liked.

Thousands of Transum Trophies are earned by pupils each week from locations across the globe. You may be surprised to hear that the top trophy earner (going by the name of Algebromaths) currently has 797 trophies in his or her trophy cabinet. Amazing!

The answer to this month’s puzzle is 10%. Sketch a Venn diagram with two overlapping circles representing blond and blue. Write x in the region representing the fraction of members with blond hair but not blue eyes. Now use the clues in the question to write the fractions of the members in the other two regions in terms of x. Now form an equation showing the three expressions you have written sum to one. Solve the equation to find x, the percentage of the choir members that do not have blue eyes.

Merry Christmas,

John

  1. Deck the halls with boughs of holly, Fa (La)9

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.

Trafalgar Square

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.

Vector Cops

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