This investigation  is a development of the caterpillar investigation and hexagon challenge, but with using multiples of 10. The shortest and longest routes can be found, but children also need to be confident enough to add several multiples of 10 together, making it suitable for around Year 3 on. The initial task of finding a route through which is less than 200 would be a good way of introducing the investigation to the whole class, perhaps using a whiteboard 10 - 50 - 40 - 70 - 20 making 190, being the smallest route. 10 - 60 - 50 - 40 - 30 - 70 - 80 - 20 making 360, being the largest route. Working in a systematic way to find all possible routes should be encouraged and children should find their own ways of recording what they have done. Once this has been completed there are a number of extensions which can be considered. The starting point could be changed - can all hexagons still be visited? Similarly, the ending point could be changed. A blank shape has been provided so that children can put their own numbers in - rather than a random selection try to suggest there is a 'theme' to their choice of numbers - all odd, all even, consecutive numbers, prime numbers etc. If hexagonal paper is available children could design their own shapes and investigate the possibilities. Go to Hexagon addition challenge