At the sundering of the world, in the empire of shade, stroll kobolds and clerics, rogues and spider queens, preparing for battles with a howling horde of death titans, fire giants and dragons of every dark and dreadful hue.

Or, looked at another way, on a table-top a complicated map is dotted with plastic figurines, moved in different directions at the roll of many-sided dice. Welcome to the world of Dungeons amp; Dragons, now, three decades after its invention, reborn as a stimulus to key stage 3 mathematics.

Twenty girls from Year 8 settle at their tables and get out their whiteboards. Liam Wegg, the head of maths at Millais School in Horsham, West Sussex, soon gets them busy multiplying by 2, 5 and 10 on the smartboard.

“Now,” says Liam, “You remember you’ve each just got your characters. We’re going to go back to what we’ve been doing the past couple of lessons, building them up through rolls of the dice. What are you, Natalie?” Natalie shakes her hair back. “A wizard.” “OK. And we’ve got dwarves, acrobats and clerics too. So, you’ll do a little experiment. If we roll five dice and take the highest three numbers and add them, then roll four dice and take the highest three and add those, which do we think will give us the highest results? Work in pairs. Write your answers on the whiteboard. And be careful of your adding up. We’re doing a lot of adding up today.”

Dungeons amp; Dragons, a grid-based war game, was published in 1977 by E. Gary Gygax and Dave Arnesen (copyrighted 1974). It kickstarted a new genre (role playing games, or RPGs), fusing tactical moves initiated by dice- rolling with imagination. Players have to develop their own characters rather than simply move in military formation. The strict ethos of the game is refereed by a storytelling Dungeon Master, whose rule book helps players resolve dilemmas, take part in battles and gather treasure and knowledge. Players gain experience points, skills and wealth to advance to different levels. Games can last for days.

Worldwide, an estimated five and half million fans play the game, whose most recent edition was published this June. Christian fundamentalists have decried it as an invocation of paganism.

Liam played it as a 13-year-old boy until he left for university. As a teacher, he says he thought: “I bet I could use this in the classroom and enjoy doing it.” He had thrown all his books away, but quickly picked up original copies on eBay. “The more I got back into it, the more I realised that there is so much in this game, from fairly simple conversion tables to advanced probability. And it’s such fun, with the characters and the social aspect.”

Liam is trialling Dungeons amp; Dragons with bottom sets in Years 7 and 8. Millais has 1,500 girls aged 11 to 16, 72 per cent of whom get five A*-C at GCSE including English and maths. A*s are high: 45 out of 300. “We do it by making them think,” says Liam, who has been head of maths for four years. “Everyone, more or less able, can think. They explain what they are doing, even at a lowish level. Then we go back and build.”

Scaling up and down, map making and orientation, conversion and probability are inherent in the game, he explains. He recommends the website of the National Centre for Excellence in Teaching Mathematics to share ideas. “We are an online community,” he says. “Everyone is keen to develop their teaching.”

There are three benefits in using a role-playing game to teach mathematics, says Liam. Players have to conform to the Dungeon Master’s edicts, helping them to learn respect for rules, they have to use their imaginations, and the purplish prose of descriptions can improve the communication skills of pupils who are not avid readers.

In the classroom, dice rolled, arms wave eagerly in the air. “Anyone got any ideas?” “Five dice were best, I think,” Fay offers. Liam nods. “So, what do we do with sets of numbers, data?” he asks. “Would you find the median?” asks Natalie. “And the mean as well?” chips in Georgia. Liam is delighted. “I didn’t intend to get into medians but the girls made the link.”

How it works

Characters in Dungeons amp; Dragons start off with a number of currency points, established by rolling different-sided dice and adding combinations of numbers. Hence the first activity.

Next, the class works on a conversion table or, as Liam calls it, a “number machine”. He is firm about the working and says: “You can’t use a calculator: they haven’t been invented yet.”

The currency is spent on equipment for adventures. Gold, silver, copper and electrum are related by multiples of 2, 5 and 10. Most girls quickly get the idea and fill in their tables. But Melissa has a problem. She is dividing instead of multiplying. Amelia can explain: “You times because you’re making 5 out of one thing.” Jess adds: “It’s the other way round from dividing.”

As the girls finish, they look up. Liam does not disappoint. “First you roll your dice to find out how much money you get, depending on your character. You haven’t all got the same. It’s not a fair world, so you have to make do with what you’ve got, until you can earn more.”

He holds up three densely typed pages. “Here is the equipment list. You spend your gold currency points to buy what you need. Don’t forget you’ll need a rucksack. You’ve got gold points, but how will you pay for something priced in copper?” Jess knows. “Use the number machine to divide?” Liam nods. “You’ve got your sheet. You can change currencies. It’s like Argos, shopping by catalogue.”

YOU CAN DO IT TOO

First, create a Dungeons amp; Dragons character.

Starter: Mental arithmetic multiplying and dividing 2, 5 and 10. Use a smartboard.

Activity 1 In pairs, roll dice in sets of four and five. Establish table of results. Extension: medians and averages. Discussion: sets of numbers.

Activity 2 Conversion tables. Discuss currency, foreign exchange and establish pupil knowledge. Concept of “number machine”. Fill in tables, individually. Discussion: difficulties.

Activity 3 Buying equipment. Hand out polygonal dice and equipment sheets. Individually, roll polygonal dice and add numbers, in different ways for different categories of characters. Use number in table to convert and buy equipment.

Next lesson Rolling dice to establish six key attributes of your character. Link to art and geography: sketches and maps of characters and terrains.

Resources

All you really need, says Liam, are the rulebooks, a character sheet for each player and a number of polyhedral dice.

You can also benefit from visiting:

www.wizards.com - Official merchandising and role-playing site, with online magazines, monster manuals, Dungeonmasters’ guides, notebooks, figurines and online communities.

www.ddo.com, www.ddo-europe.com - Commercially run community sites.

www.dnd4.com - Up-to-date guide to the latest edition.

www.indie-rpgs.comarticles20 - A history of the game by an enthusiast.

www.wickeddice.co.uk - For all kinds of dice.

www.ncetm.org.uk - National Centre for Excellence in the Teaching of Mathematics: ideas for unusual maths.