Published by JR Books

Rob Eastaway’s book, subtitled “Surprisingly interesting everyday maths”, is a gentle introduction to a variety of maths problems, typified by the puzzle from which the book takes its title: how many socks do you need to pull from a draw to be sure to get a matching pair.  The problems are developed to explore mathematical creativity, to draw out the “Beauty, Discovery and Humour” as Koestler described how creativity manifests itself, or the “Ah, Aha! and Haha of mathematics” as Eastaway neatly paraphrases.

Topics include the riffle shuffle, the dimensions of A-sized paper, magic squares and the location of the centre of Britain (exploring the centre of a triangle).

Idea for the classroom: The Saddam Puzzle (Chapter 5)

100 prisoners are told that the next day, they will be buried up to their necks in sand, in a line so the one at the back can see the 99 in front, then the next can see 98 and so on.  Each prisoner will have either a black or a white hat placed on his head.  Starting at the back, each prisoner in turn then has to shout out the colour of their own hat.  If they get it right, they are spared.  If they don’t, they aren’t!

How can the prisoners form a plan to save as many people as possible?

Published by Allen Lane

Lewis Carroll’s “fantastical mathematical logical life” is charted from his birth in Cheshire through to his academic career at Christ Church, Oxford.  Along the way, Carroll’s mathematical puzzles and diversions are explored as well as other aspects of his life – such as his contribution to the development of photography.  We meet characters from the Alice books as well as the wide range of Carroll’s interests – from the logic puzzles and his invention of Carroll diagrams to solve them, to different methods for voting in elections.

Idea for the classroom:  Fit the Third, Three Tricks

Three number tricks are described – explore them to discover how and why they work, giving lots of practice in arithmetic and insight into the number system.

The addition sum: I asks you for a 4 digit number, eg. 2879; I then write down another number (22877) and hide it;  We take it in turns to propose 4 more numbers (eg. you say 4685, I say 5314, you say 7062, I say 2937); add the five numbers together to get the hidden total.  What numbers should I choose?

Counting alternately to 100 (a Nim-type game): start at 1 and take it in turns to add a new number from 1 to 10; the person who reaches 100 is the winner.  How can you make sure you always win?

The “9″ trick:  You choose a number, reverse it and subtract the smaller number from the larger.  Remove any digit (except 0) from the answer and tell me the sum of the remaining digits.  I can then tell you which digit you removed.  How?

Published by 4th Estate, 2008

Ben Goldacre – doctor, blogger and Guardian columnist - gives an entertaining and informative introduction to the scientific method for medical research and debunks a wide range of charlatans and dodgy practice.  He explains why poor journalism and a lack of scientific understanding has allowed health scares to develop and how different individuals have taken advantage, with topics including detox, nutritionists, homeopathy, Gillian McKeith, Patrick Holford, Brain Gym, MMR, antioxidants and MRSA.

Idea for the classroom:  Chapter 13 Bad Stats

Examples are given of how statistics and probability can be used (and misused) – tests for diseases, miscarriages of justice, the prosecuter’s fallacy.  Use these examples with A level students doing Statistics, ask them to explore the maths involved and challenge them to explain the ideas behind these misconceptions to a non-maths specialist.

Published by Profile Books, 2008

Ian Stewart collects together an assortment of recreational maths – jokes, puzzles and introductory articles on a wide range of maths topics.  If you have read your share of maths books, there are not a great deal of original ideas here.  However, dipping in anywhere will remind you of puzzles you had forgotten or introduce an area of maths you had heard of or studied a long time ago.  Checking the answers will lead you off to thinking about the maths underlying the problems and there are web addresses to follow and numerous starting points to explore further.

Idea for the classroom:  Deceptive Dice (page 36)

Three dice with different numbers on: Yellow has 1, 5 and 9 (each on two faces), Red has 3, 4 and 8 and Blue has 2, 6 and 7.  Two players each pick a dice, roll and the winner is the one with the higher score.  Which is the best dice?  Could use this as an investigation – in groups, investigate one pairing (eg. Yellow v Red) – do trials, construct sample spaces etc.  Then send one member of each group to the other groups to share results.  Can you explain the surprising outcome?

Give everyone a piece of A3 paper, fresh from the photcopier. Fold it to A4, then A5 and finally A6. Then unfold it, so there are 16 spaces, 8 on each side.

Write the numbers 1 to 16 in the spaces, then for each number, add as many calculations, words, or diagrams that are associated with that number. For example, for the number 9 you could have 5 + 4, 3 x 3, 9 dots in a square pattern, multiples of 9: 18, 27, 36, … , a nonagon etc.

Once everyone has written their ideas down, share ideas in pairs and then in fours. Give everyone a piece of A4 and everyone chooses a number. They draw the number in the middle of the page then add their ideas for that number. Take a survey to see which numbers haven’t been chosen, and anyone who finishes can do one of those numbers. Use the numbers to make a classroom display.

Find ideas for lessons, try them out and discuss the outcomes.