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8. Patterns
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AustraliaNSW
Stage 2

8.05 Matchstick patterns

Lesson
Practice
Lesson

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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 pattern of squares. The first figure has 4, the next has 6, the next has 8. Ask your teacher for more infomation.
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.

\displaystyle 8+2\displaystyle =\displaystyle 10Add 2 to 8
\displaystyle 10+2\displaystyle =\displaystyle 12Add 2 to 10
\displaystyle 12+2\displaystyle =\displaystyle 14Add 2 to 12

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:

\displaystyle 6-4\displaystyle =\displaystyle 2Subtract the first number from the second
\displaystyle 8-6\displaystyle =\displaystyle 2Subtract the second number from the third

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.

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Examples

Example 2

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

A pattern of matchsticks that represent the numbers 6, 11 and 16. Ask your teacher for more infomation.
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.

\displaystyle 16+5\displaystyle =\displaystyle 21Add 5 to 16
\displaystyle 21+5\displaystyle =\displaystyle 26Add 5 to 21
\displaystyle 26+5\displaystyle =\displaystyle 31Add 5 to 31

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

MA2-6NA

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

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