# Making generalisations

Developing fluency with number facts requires not only the ability to recall facts, but also an understanding of the:

• commutative property (i.e. 3 $$\times$$ 4 and 4 × 3 are equivalent)
• distributive property (e.g. 6 $$\times$$ 8 = 6 $$\times$$ 5 + 6 $$\times$$ 3)
• relationship between multiplication and division.

Activities can provide opportunities to build up a range of strategies such as:

• doubling and halving
• commutativity
• partitioning numbers into known facts using distributive property.

These strategies assist in developing number fact fluency and flexibility.

Discussions about the facts students know and do not know can assist in building up further facts.

For example, knowing 10 $$\times$$ 5 can assist in working out 9 $$\times$$ 5, 5 $$\times$$ 5, 10 $$\times$$ 50.

Useful resources include:

• rectangular arrays
• a 1–100 grid
• multiplication fact grid
• triangle flash cards (card with the number at the top and the two factors in either corner).

## Investigating patterns

In this activity, students construct a rectangular array for a given number from which they will generate and record the multiplication facts and the list of factors.

## Facts within facts

In this activity, students draw on their knowledge of known facts, doubles and partitioning to identify related facts within facts.

## Divisibility patterns

In this activity, students draw on their knowledge of factors and known multiplication and division facts to determine which whole numbers are divisible by 2, 4, 5 or 10.