This investigation is aimed at younger children, probably years one or two, although it can be used with older children to explore all possible combinations and reflections. There are many routes through the caterpillar, the shortest possible going through 5 circles. How many different ways of going through 5 circles can be found? How can these be recorded? Useful resources: Nine large circles cut out of card. Photocopied sheets of blank caterpillars  (see aworksheet). Coloured pencils or crayons. Large 0 - 9 number cards. Smaller circular cards joined by split pins. Ways of recording: Children could colour or number the different routes:  eg 6 circle routes: or Encourage: Working in a systematic way - counting up to 9. Checking to see that the same route has not been repeated. Exploring what would happen if the head and tail were placed in different positions. Go to Caterpillar Counting Investigation