# Number fact fluency

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.

## Facts and models

In this game, students draw on their knowledge of fact families to generate multiplication and division facts.

## What do I know?

In this activity, students build up a list of facts they can recall automatically. They discuss some possible strategies to deal with those that they do not know or need to use additional thinking to work out.