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You might like to play the factors and multiples game before attempting this investigation, which can be taken to many levels of complexity.
Write down a selection of positive whole numbers less than 100 in some positions of your choice on a large blank piece of paper.
Now, draw lines (not necessarily straight) which join each number in the selection with all of the factors and multiples of the number in the selection.
For your selection and arrangement of numbers, can you draw lines so that none cross?
Explore!
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
Explore some of the different types of network, and prove a result about network trees.
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.