Students are first introduced to multiplication through problems involving groups of equal size:
3 x 4 = 12
They then move on to arrays:
3 x 4 = 12
To understand multiplication, students need to recognise that the array represents three groups of four (and also four groups of three). (Students who struggle with mathematics are often unaware of patterns that are obvious to others.) Once the relationship between arrays and multiplication is established, students can apply their understanding to area, for example, by finding the number of squares in a rectangle:
3 x 4 = 12
Once students understand area as length x width, they can generalise this and move beyond small whole numbers to large whole numbers and decimal fractions:
- If the area of a 3 cm x 4 cm rectangle is (3 x 4) cm2, then the area of a 3000 cm x 4000 cm rectangle is (3000 x 4000) cm2.
- We can’t show 4.8 groups of 7.3 items in array; the counting model has reached its limitations. We can, however, create a rectangle with side 4.8 cm x 7.3 cm and find its area.
Area is 4.8 x 7.3 = 35.0 cm2