Newsletter

Sisters Outnumber Brothers

Tuesday 1st February 2022

This is the Transum Newsletter for the month of February. It begins, as usual with the puzzle of the month.

Rachel has the same number of brothers as she has sisters. Each one of her brothers has 50% more sisters than brothers.

How many children are in Rachel's family?

The answer will be at the end of this newsletter.

February highlights for Maths teachers: The 1st February is the first day of the Chinese New Year so you might raise awareness by playing the Chinese game of Pong Hua K'l, Valentine’s Day is on the 14th and who doesn’t Love Maths? A few days later on the 22nd we have a Palindromic date (22-02-2022). Many famous mathematicians have February birthdays including Galileo Galilei, Copernicus, Hardy, Bernoulli and of course the wonderful Hannah Fry. February this year has exactly four weeks so the 1st February falls on the same day of the week (Tuesday) as the first day of the following month which is quite unique.

 

I spent the recent holiday with my parents in the UK. Mom loves to watch the quiz shows on the TV so I was rapidly brought up to speed with The Chase, Catchphrase and University Challenge. The programme that set me thinking however was called Lingo. Contestants have to guess words from clues about the letters in that word. I have since discovered that there is a viral web based version of the puzzle called Wordle. A small light bulb appeared over my head and I came up with Equatero, the mathematical expression version aimed at school students. The principle is the same as Mastermind, a game I remember from my youth, but my version consists of numbers and mathematical symbols.

As soon as the code was written and the activity was working well I had another lightbulb moment. A few changes to the code and I had another activity that I called Vocabero. This was similar to the game I saw on TV but was limited to mathematical words. It made a nice addition to the Transum Maths Vocabulary activities.

The Rowcol Game is not only brand new but also completely original. It is fascinating to come up with an idea for a game then develop it through various versions, tweaking the way the game works in order to give the most interesting, exciting and thought-provoking experience for the players. A good strategy might direct a player not to always claim the highest value token if thinking one or two moves ahead reveals a more profitable decision.

 

Have you seen the Leapfrog investigation? It's a challenge to find the minimum number of moves to swap the positions of the blue and green frogs by encouraging them to leap from one lily pad to another. This really is one of the old-school investigations. I remember in the early eighties, when investigations suddenly became a ‘thing’, this was one activity that I did in the classroom with pupils acting as the frogs sitting on a row of chairs arranged at the front of the classroom. There have been a number of computer-based versions over the years and I’d been using a Flash version on Transum but now that Flash has been banished from browsers I have created an updated version in JavaScript.

The basic part of the investigation will reveal a quadratic sequence but can you find the rule for the nth term? The investigation can be extended with unequal numbers of blue and green frogs or different numbers of lily pads.

“What number is that which being diminished by one-seventh of itself will equal 162?” Don’t you love the style in which maths problems used to be written? A new level 7 has been added to the Algebra in Action set of exercises which were taken from A First Book in Algebra, by Wallace C. Boyden published in 1895.

There are many mathematical facts that have to be memorised and an excellent way to make this part of learning engaging is by playing one of the Pairs games. Transum has interactive pairs games on many topics (30 so far) including Formulas to Remember, Names of Circle Parts and, just added last week, Greek Letter Pairs. I have chosen the 10 letters that I come across most frequently and created this card came to help students learn their names.

 

Have you taught the topic of collecting data using surveys? Pupils should be aware of the way to ask questions and how to find a representative sample in order to get reliable results. Tim Harford from the More or Less podcast set up a poll in Twitter to ask if Twitter polls were useful or useless. 75% of respondents said useless. Does this result make the poll useful? Or is this a paradox? I’m guessing this would make a great class discussion. I’ve included the audio on the Transum Podcast for this month.

Finally the answer to the puzzle of the month:

Let Rachel have n brothers and n sisters.

There are n boys and n+1 girls in Rachel’s family.

Each boy will have n-1 brothers and n+1 sisters so n+1 is 50% more than n-1.

This can be written as n+1 = 1.5(n-1)

2(n+1) = 3(n-1)

2n+2 = 3n – 3

n = 5

There are 2n+1 children in Rachel’s family which equates to 11.

That's all for now,

John

P.S. If a got 50 pence for every time I failed a maths exam I'd have about £6.30 now.

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