Topics
6. Multiplication and division
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Australia
Year 3

6.04 Fact families

Lesson
Practice
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.

An array of circles with 4 rows and 10 columns. Each row of 10 circles are in a rectangle.
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.

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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
An array with 5 rows and 1 column.

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

AC9M3N04

multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams and arrays, and using a variety of calculation strategies

AC9M3A03

recall and demonstrate proficiency with multiplication facts for 3, 4, 5 and 10; extend and apply facts to develop the related division facts

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