So different arrangements will prompt different strategies, and these strategies will vary from person to person. Seeing the objects for only a few seconds challenges the mind to find strategies other than counting. To begin with, early number activities are best done with moveable objects such as counters, blocks and small toys. Most children will need the concrete experience of physically manipulating groups of objects into sub-groups and combining small groups to make a larger group. After these essential experiences more static materials such as 'dot cards' become very useful.
Dot cards a simply cards with dot stickers of a single colour stuck on one side.
The important factors in the design of the cards are the number of dots and the arrangement of these dots. The various combinations of these factors determine the mathematical structure of each card, and hence the types of number relations and mental strategies prompted by them. Consider each of the following arrangements of dots before reading further. Card A is the classic symmetrical dice and playing card arrangement of five and so is often instantly recognised without engaging other mental strategies. It is perhaps the easiest arrangement of five to deal with.