# 6.04 Fact families

Lesson

## Are you ready?

We can use  arrays  to help us in this lesson. Let's try this problem to review.

### Examples

#### Example 1

Complete the statement with the missing numbers: There are groups of counters.

Worked Solution
Create a strategy

Count the number of counters in each group. Each rectangle is 1 group.

Apply the idea

There are 10 counters in each rectangle, and there are 4 rectangles.

There are 4 groups of 10 counters.

Idea summary

Arrays can be used to group objects and show multiplication and division.

## Fact families for multiplication and division

This video introduces fact families for multiplication and division facts.

### Examples

#### Example 2

Complete the fact family with the missing numbers.

\begin{aligned} 5\times⬚&=5 \\ 1\times⬚&=5 \\ 5\div⬚&=5 \\ ⬚\div5 & =1 \end{aligned}

Worked Solution
Create a strategy

Use this array which can be thought of as 1 column of 5, or 5 rows of 1.

Apply the idea

The array shows that 5 rows of 1 square gives 5 squares. This gives us: 5\times 1 =5

The array also shows that 1 column of 5 squares gives 5 squares. This gives us: 1\times 5 =5

The array also shows that if we divide 5 squares into 1 column there will be 5 squares in the column. This gives us: 5\div 1 =5

The array also shows that if we divide 5 squares into 5 rows there will be 1 square in each row. This gives us: 5\div 5 =1

So we get: \begin{aligned} 5\times1&=1 \\ 1\times5&=5 \\ 5\div1&=5 \\ 5\div5 & =1 \end{aligned}

Idea summary

For a multiplication problem such as 4\times3=12, we can write 3 other facts to form the fact family: \begin{aligned} 3 \times 4&=12 \\ 12 \div 3&=4 \\ 12 \div 4 & =3 \end{aligned}

### Outcomes

#### MA2-6NA

uses mental and informal written strategies for multiplication and division