 # 8.05 Matchstick patterns

Lesson

## Ideas

A picture can often help us to see how the numbers are changing in a pattern.

### Examples

#### Example 1

The number of squares in the picture represents the numbers in the pattern. Write the next numbers in the pattern.

a

4,\,6,\,8,\, ⬚,\, ⬚,\, ⬚

Worked Solution
Create a strategy

Count the squares being added each time.

Apply the idea

The number of squares being added each time is 2.

So, we can complete the pattern by adding 2\,to the numbers.

The complete pattern is 4,\,6,\,8,\,10,\,12,\,14

b

Which of the following best describes the pattern above?

A
The numbers are doubling.
B
The numbers are increasing by 2.
Worked Solution
Create a strategy

Find the difference between the numbers to describe the pattern.

Apply the idea

Subtract numbers that are next to each other in the pattern:

The numbers in the pattern is increasing by 2. The correct option is B.

## Matchstick patterns

Let's look at some real life examples of how we can find patterns using matchsticks.

### Examples

#### Example 2

Write the next numbers in the pattern about the number of matches used to make the pattern.

a

6,\,11,\,16,\, ⬚,\,⬚,\,⬚

Worked Solution
Create a strategy

Count the number of matches being added each time.

Apply the idea

The number of matches being added each time is 5.

So, we can complete the pattern by adding 5\,to the numbers.

The complete pattern is 6,\,11,\,16,\,21,\,26,\,31

b

Which of the following best describes the pattern above?

A
The numbers are increasing by 4
B
The numbers are increasing by 5
Worked Solution
Create a strategy

Find the difference between the numbers to describe the pattern .

Apply the idea

The change in the pattern can be described by calculating 11- 6 = 5.

The number in the pattern is increasing by 5. The correct option is B.

Idea summary

Sometimes drawing a picture to represent a pattern can help us to understand how the numbers are changing.

### Outcomes

#### MA2-8NA

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