Magic
numbers
Tuesday April
8, 2008
Maths
Inspiration aims to show teenagers how much fun it can be -
as well as a valuable tool for the future.
Rob Eastaway grins at his teenage audience. "Here's how to
win a bet at the pub - if you're allowed in, of course."
Giggles and murmurs as he rattles through demonstrations of
card shuffles, newspaper predictions, coin tricks and the
likelihood of people lying. "It's maths masquerading as
magic," he explains, going on to debunk TV magician Darren
Brown's "psychology" as cheapjack probability.
The audience is gripped, texting quick tips to friends on
silenced mobiles as they marvel at the Gilbreath shuffle (a
way to ensure that a stacked deck stays stacked), Benford's
Law (which predicts that in most sets of numbers those
beginning with 1 have a 30% greater likelihood of appearing
than others, and Penney Ante (a coin-flipping con-trick
described by Walter Penney in 1969).
Several hundred year 10, 11 and 12 students have come into
Southampton for a maths field trip. They were sceptical -
15-year-old Simon Preston and his mates at Gregg College
thought "it was going to be really boring" - but after an
interactive three hours decoding puzzles, learning how to
build sports stadiums and quizzing speakers on embarrassing
maths moments, the crowd of teenagers bounces out of the
lecture hall agreeing with 17-year-old Alice Pinkley from
Havant College: "It was entertainment as well as maths, and
you don't usually get that."
While the government bemoans the lack of keen young
mathematicians in schools and sets up the National Centre
for Excellence in Teaching Mathematics (NCETM), Eastaway,
together with his friend and co-populariser Simon Singh
(author of Fermat's Last Theorem and The Code Book), has
been running Maths Inspiration events since 2004. "As a
nation, it's numbers and creativity and hard work that can
save us from stiff competition from India and China," says
Eastaway, who was until recently president of the
Mathematical Association. This year, more than 8,000 people
attended 11 events. Eastaway believes that the way to grow
more mathematicians is to tap into popular culture and
share the playfulness of mathematics as well as its rigour
and purity.
That's why he mixes parlour tricks with the hard maths of
statistics and random patterns, interspersing good old
shortcuts like how to calculate the square of any two-digit
number in your head (see below). A sharp seasoning of
career prospects doesn't hurt, either: a hubbub greets the
news that, on average, graduates with maths-related degrees
earn 5-10 times as much as non-maths graduates. "We want to
get them when they're thinking about whether to take maths
further," he explains. "At year 11 and 12 all you've ever
seen of maths is the classroom: we want them to have a
field trip and come back with the news of maths in the real
world."
Pete Shepherd is an engineer who helped to build the
Arsenal Emirates and Dublin Lansdowne Road stadiums. His
real-world maths mixes facts like how many elephants it
takes to fill the Emirates (710) with computer-modelling of
material resonance to avoid stands built with a frequency
harmonic with human activity - which could lead to
collapse. Equally real are the rewards of world travel and
telling football-watching friends "Look up: I built that!"
Gina Hall, director of learning at St Edmund's RC high
school, Southampton, enthuses: "That's why we brought our
year 11s, to broaden their horizons. In the bus, they were
full of elephants in the stadium and how you shuffle cards
- but also that there are interesting jobs in maths."
Simon Singh's passion for decoding and demystifying targets
mathematical imaginations. "Your teachers are doing a great
job giving you bread and butter maths," he says, "but risk
and probability: wherever you go, whatever you do, you'll
encounter them. Maths is thinking logically, critically,
analytically, creatively - about anything."
The students are impressed. Preston says: "The way he
thought of other ways of looking at things was really
inventive."
For undecided students, like the year 10 set brought from
Medina College on the Isle of Wight by the head of maths,
Jane Griffiths, the afternoon offered "creativity and
stimulus, which are so important. At GCSE they don't see
the bigness of it, to see that it's worth studying for its
own sake".
Eastaway, who has been visiting schools since the surprise
success of his book Why Do Buses Come in Threes? (1997),
sees four worries in maths education: the frequent "what's
the point?" complaint of pupils; myriad distractions; an
unwillingness to follow repetitive procedures that do serve
to embed useful mental tools; and little knowledge of the
recreational side of maths. "At school I read around the
subject," he says. "I read Martin Gardner, Scientific
American; I used to devour the curiosities. These all seem
to have disappeared. Things we used to talk about at lunch,
they were interesting outside lessons."
Maths Inspiration was born to fill that gap. Is it about
fun? Eastaway winces. "It is not just fun but interesting.
It makes you want to explore further."
Back on the Isle of Wight, Griffiths was amazed to find six
year 10s come into class the next day and say, "Can we take
this lesson?" They brought newspapers in to do trials of
Benford's Law. They even remembered Eastaway's square
exercise when practising a GCSE non-calculator paper. "Most
were bewildered, but the ones who'd been to Maths
Inspiration said, 'This is how you do it.' They were fast!
Some even came up with the geometric explanation, which
they'd worked out themselves. We're definitely going again
next year."
How
to square a number in your head
Say we want to do the sum 98 x 98 in our heads. The trick
is to make this easier by turning it into much simpler
sums.
Round the number 98 to the simplest number close to it -
100
Having added 2 to one of the 98s, remove 2 from the other,
to give the sum:
100 x 96 (= 9600)
Now square the difference (2 x 2=4) and add that to the
answer, to give 9604
Similarly:
96 x 96= (92 x 100) + (4 x 4) = 9216
And to be really ambitious ...
To square 61 x 61, turn it into ...
(50 x 72) + (11 x 11)
= 3600 + 121 =3721
Why it works:
(a - b) x (a + b) = (a x a) - (b x b) hence
a x a = (a - b) x (a + b) + (b x b)
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