Recognising, Describing and Continuing Number Patterns
A number pattern is a sequence of numbers that follows a rule. Recognising and describing patterns helps predict future values and understand how numbers are related.
Patterns may involve addition, subtraction, multiplication, division or a combination of these.
Recognising Number Patterns
To recognise a pattern, look at how each number changes to the next.
For example:
$$
2,\ 5,\ 8,\ 11,\ 14
$$
Each number increases by \( 3 \). This is an additive pattern.
Another example:
$$
81,\ 27,\ 9,\ 3
$$
Each number is divided by \( 3 \). This is a multiplicative pattern.
Some patterns alternate between two rules.
For example:
$$
2,\ 4,\ 3,\ 6,\ 5,\ 10
$$
The pattern is multiply by \( 2 \), then subtract \( 1 \).
Describing Number Patterns
A pattern should be described clearly using words and, where appropriate, numbers.
For example, the pattern:
$$
5,\ 10,\ 15,\ 20
$$
can be described as:
“Start at 5 and add 5 each time.”
Another example:
$$
3,\ 6,\ 12,\ 24
$$
can be described as:
“Start at 3 and multiply by 2 each time.”
Clear descriptions are important so that the pattern can be followed correctly by someone else.
Continuing Number Patterns
Once the rule is known, the pattern can be continued.
For example, for the pattern:
$$
7,\ 14,\ 21,\ 28
$$
The rule is add \( 7 \), so the next two numbers are:
$$
35,\ 42
$$
For a multiplicative pattern:
$$
4,\ 12,\ 36
$$
The rule is multiply by \( 3 \), so the next number is:
$$
108
$$
Patterns Involving Fractions and Decimals
Patterns can also involve fractions or decimals.
For example:
$$
1,\ 0.5,\ 0.25,\ 0.125
$$
Each number is divided by \( 2 \).
Another example:
$$
0.2,\ 0.4,\ 0.6,\ 0.8
$$
Each number increases by \( 0.2 \).
Key Points to Remember
Look for the change between terms to identify the rule.
Describe patterns clearly using words.
Use the rule consistently to continue the pattern.
Patterns may involve more than one operation.
Recognising and working with number patterns builds confidence with sequences and prepares for algebraic patterns and formulae later on.