Stage 1: numbers, counting, sorting, matching, and arranging in order

Children should first learn to count and to recognize numbers. They should then sort objects into groups, before learning to match objects by size, colour, and shape. They should then learn how to arrange numbers in order.

Stage 2: addition, subtraction, multiplication, and division

Adding is a form of counting (2 + 2 is another way of saying, start with two and then count a further two). Children may need to use concrete objects (such as blocks or fingers) at first.

Subtraction is counting backwards (5 - 2 is another way of saying, start with five and then count two backwards). Children are often taught adding and subtracting using a number line (Figure 8.1).

Figure 8.1 A number line.

Children are usually encouraged to learn the link between addition and multiplication before memorizing multiplication tables (2 x 3 is another way of adding two sets of three).

Division is often introduced as sharing (8 ^ 2 is eight apples shared between two children).