topic badge

7.05 Patterns 1

Lesson

Are you ready?

Do you remember how to use  repeated addition  to solve multiplication?

Examples

Example 1

Write this addition as a multiplication.

4+4+4+4

Worked Solution
Create a strategy

Rewrite the addition as a multiplication in this form:

Number of groups \times amount in each group

Apply the idea

We are adding 4 groups of 4.

4+4+4+4= 4 \times 4

Patterns with multiplication

When we need to multiply, it can help to see if there are any patterns that help us. Let's look at some in this video.

Loading video...

Examples

Example 2

Complete the following pattern.

Start at 8 and double the answer each time.

8, \,⬚, \, ⬚, \, ⬚

Worked Solution
Create a strategy

Doubling is the same as multiplying by 2.

Apply the idea
\displaystyle 8 \times 2\displaystyle =\displaystyle 16Multiply 8 by 2

To multiply 16 by 2 we can use a vertical algorithm:

\begin{array}{c} & &1 &6 \\ &\times && 2 \\ \hline \\ \hline \end{array}

First we multiply 2 by 6 which is 12. So we put 2 in the units column and carry the 1:\begin{array}{c} & & {}^1 1 &6 \\ &\times && 2 \\ \hline &&&2 \\ \hline \end{array}

Multiply 2 by 1 and add the carried 1 to get 3. We put this in the tens column:\begin{array}{c} & & {}^1 1 &6 \\ &\times && 2 \\ \hline &&3&2 \\ \hline \end{array}

To multiply 32 by 2 we can use a vertical algorithm and multiply 2 by 2 to get 4 in the units column: \begin{array}{c} & & 3 &2 \\ &\times && 2 \\ \hline &&&4 \\ \hline \end{array}

Multiply 2 by 3 to get 6. We put this in the tens column: \begin{array}{c} & & 3 &2 \\ &\times && 2 \\ \hline &&6&4 \\ \hline \end{array}

The complete pattern is 8,\,16,\,32,\,64.

Idea summary

When we find a pattern with multiplying, we can use that to solve other multiplication problems.

Outcomes

MA2-6NA

uses mental and informal written strategies for multiplication and division

MA2-8NA

generalises properties of odd and even numbers, generates number patterns, and completes simple number sentences by calculating missing values

What is Mathspace

About Mathspace