Exploring patterns and relationships assists students to:
- develop a range of strategies
- build up a bank of known facts
- build an awareness of number properties, such as commutativity and identity.
Students can make generalisations from patterns.
For example, in a rectangular grid the structure of 3 rows of 4 columns or 4 columns of 3 rows can lead to generalising 3 \(\times\) 4 = 4 \(\times\) 3 which is the commutative property for multiplication.
Use a 1–100 number grid in a 10 by 10 shape to explore sequences of multiples by shading each multiple in a different colour.
This can lead to generalisations, such as every second multiple of 2 in the twos' sequence (2, 4, 6, 8, 10, 12…) is also a multiple of 4.
Students could see if the same relationship exists for any other multiples (e.g. threes and sixes; fives and tens).
Identifying the patterns that exist within the multiplication facts can assist students to identify and generalise divisibility patterns. For example, a number is divisible by five if it ends in a five or zero.
