Then when I asked them to tell me what they were, they realised that there was only one way. So then I asked how many different ways they could get 16, and using their previous rule, they suggested 15 ways. So then I jumped to the other end of the distribution, asking “What is the strongest team we could possibly get?” As it happened, they did have two dragons of strength 8 in their set of dragons, so they correctly estimated the answer to be 16. How many ways to get strength 3? By the time we got to strength 6, they could see a pattern, that the number of combinations is one less than the total strength.

It is not possible to have a team of strength 1, and there is only one way to get a team of strength 2. What I did do, was start working out how many different combinations were possible. I should have explored this idea further. After they had made an attempt at solving it, I asked what they thought would be the most common team strength, and one said 9 or 10 because it is in the middle. Recently I used this task with a group of ten-year-olds. You can also discuss what “nearly always” means. You can have discussions about what it means for the dragons to be chosen randomly. Then they need to work out a recording method, possibly a tally table. This is sometimes called “low floor, high ceiling”.For younger children, it is a good start to take pairs of dragons, add their strengths, and write down the answer. It has a low entry point, as encouraged on Youcubed.

What is great about this exercise is that you can explore it experimentally or theoretically. Like Tracy Zager, we emphasise the necessity of exploring the maths ourselves before the children. If you do not have any dragons of your own, make up about 20 pieces of card, with the numbers 1 to 8 on them, so you can explore the problem. Provide evidence to support your conclusion. The taskĪ dragon team trainer says that teams of two dragons chosen at random nearly always have a combined strength of between 7 and 11. Some may or may not have dragons of each strength rating. As there are a total of 288 dragons, each group will have a different set of dragons. The students will already be familiar with the dragon cards, and each group of students has a set of about 24 dragonistics data cards. The distribution of dragon strengths is not uniform, but is clustered around the middle, and depends to a certain extent on other aspects of the dragon, such as their species, gender and behaviour. A small sample of Dragonistics data cardsĮach dragon has a strength rating of between 1 and 8, shown by the coloured dragon scales on the right-hand side of the card.

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