Take the roulette wheel for a spin to get children interested in probability, says John Dabell
What's the betting that using a roulette wheel in a maths lesson is likely to make most colleagues twitchy? Surely going down this path is encouraging children to gamble? Well, quite the reverse. When roulette is seen as a game of chance ruled by probability then the likelihood of breeding a class of addicts is very low. As Albert Einstein once said: "You can't beat a roulette table unless you steal money from it."
Roulette was devised in 17th-century France by the mathematician Blaise Pascal, who was inspired by a fascination for perpetual-motion devices.
Roulette means "small wheel". It is a game of chance with the object of guessing where a ball spinning on the roulette wheel will land. The croupier rolls a ball along the inner edge of the wheel in the opposite direction of its spin. As the wheel turns, the ball loses momentum and bounces between numbered slots. The slot where the ball finally comes to rests is the winning number for that game.
A roulette wheel has 38 slots, numbered 1 through 36, 0 and 00. Two of the slots are coloured green, 18 red and 18 black. Gamblers often bet on a red number. If they wager pound;1 on red and the roulette ball lands on red then they win pound;1, but if it lands on green or black they lose pound;1. There are 18 red slots out of the total of 38, so the chances of winning are 1738, which is less than even.
A toy roulette wheel is cheap and can easily be used for maths. A worthwhile investigation is to challenge children to come up with their own rules for the game, using counters. Children work out whether each number from 1 to 36 is a prime, composite, triangle, square or cube number. They then calculate the probability of spinning each number. They will soon see that the probability of spinning a composite number is high and it is little wonder that the casinos shy away from making that one of their games. See the table, above.
The challenge from here is to generate some rules about how many counters you can win according to the number that comes up. For example, if a 1 or 36 comes up then, because these numbers can be classified three ways as triangle, square and a cube, then that could mean you triple what you placed as you bet. If you bet 10 counters then you win 30 counters plus your 10 back.
What next? Well if each new spin is a new spin and the outcome is never determined by prior spins then what are the odds of spinning lucky number 7 four times in a row? This is a rarity. In fact the sequential probability of four 7s coming up in a row is very high (138 x 138 x 138 x 138 = 12,085,136), but the absolute probability of number 7 to come up at each spin is always 1 in 38. Do particular numbers come up more than others?
Roulette doesn't have to be played in the traditional way. How about playing it as a game of bingo using mathematical clues, with specially designed bingo cards for children to complete.
Examples of clues might be:
l2 = the only even prime number;
l7 = a score minus a baker's dozen;
l16 = a heptagon plus a nonagon;
l28 = three more than the fifth square number;
l34 = a quarter of 136.
Individual numbers can themselves be fascinating. For example, 28 is both a triangle number and a composite number. It is also a perfect number, since it is equal to the sum of its divisors: 1 + 2 + 4 + 7 + 14 = 28. Which other roulette number is also a perfect number?
Roulette might not be your first choice to improve children's maths but it does have great potential to improve number knowledge and understanding.
Try it for yourself - it's sure to cause a bit of interest and get everyone thinking about numbers.
One thing to ponder: if you add together all the numbers from 1 to 36, which number do you get? Maths can be devilish at times.