Describe & continue number patterns
Theory
Describing and continuing number patterns is a Year 3 maths skill: finding the step in a pattern, describing the rule in words such as add 3 each time or take away 4 each time, and using it to continue the pattern or find a missing number. This page shows patterns on number lines, in tables and as growing shapes. In the Australian Curriculum, adding and taking away patterns start in Year 2 (AC9M2A01) and are extended in Year 3. Curriculum: VC2M3N09 / AC9M3N07.
A number pattern is a list of numbers that follows a rule. The rule tells you how to get from one number to the next. In \(1,\ 4,\ 7,\ 10,\ \ldots\) each number is 3 more than the one before. Each number in a pattern is called a term.
The step is the amount you add or take away to move from each number to the next. To find it, look at the jump between two numbers next to each other. Then you can describe the rule in words, like "add 3 each time" or "take away 4 each time".
An add pattern grows because you add the step, like \(4,\ 9,\ 14,\ 19\). A take-away pattern shrinks because you subtract the step, like \(24,\ 20,\ 16,\ 12\). Once you know the step you can continue the pattern or find a missing number.
Every number pattern has a start number and a step. These facts show how to use them.
A pattern can also be shown in a table. Each position has a value, and the value goes up by the step each time.
| Position | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Value | 6 | 9 | 12 | 15 | 18 |
How to describe and continue a number pattern
- Find the step. Look at two numbers next to each other and work out the jump between them.
- Check the direction. If the numbers grow, the rule is "add" the step; if they shrink, the rule is "take away" the step.
- Use the same step. Add or take away that step to continue the pattern, fill a missing number, or find what comes before the start.
| \(13 - 8\) | \(=\) | \(5\) |
| \(18 - 13\) | \(=\) | \(5\) |
Each jump is \(+5\), so the rule is add 5 each time.
| \(50 - 45\) | \(=\) | \(5\) |
| \(35 - 5\) | \(=\) | \(30\) |
The numbers go down by 5, so the next number is \(30\).
| \(\text{each jump}\) | \(=\) | \(+4\) |
| \(15 + 4\) | \(=\) | \(19\) |
The next jump lands on \(19\).
| \(5 - 2\) | \(=\) | \(3\) |
| \(8 + 3\) | \(=\) | \(11\) |
Each picture adds 3 dots, so the 4th picture has \(11\) dots.
Common pitfalls
Frequently asked questions
What is a number pattern?
A number pattern is a list of numbers that follows a rule. The rule tells you how to get from one number to the next, usually by adding or taking away the same amount each time.
How do you find the rule of a number pattern?
Look at two numbers next to each other and work out the jump between them. If each number goes up by 3 the rule is "add 3 each time". If each number goes down by 5 the rule is "take away 5 each time".
How do you continue a number pattern?
First find the step, then keep using it. For \(8,\ 14,\ 20,\ 26\) the step is add 6, so the next number is \(26 + 6 = 32\).
What does add 3 each time mean?
It means every number in the pattern is 3 more than the number before it. Starting at 2 you get \(2,\ 5,\ 8,\ 11,\ 14\) and so on.
How do you find a missing number in a pattern?
Find the step from two numbers you can see, then add or take away that step. In \(9,\ 15,\ \underline{\ \ },\ 27\) the step is 6, so the missing number is \(15 + 6 = 21\).
What is the difference between an add pattern and a take away pattern?
An add pattern grows because you add the step each time, like \(4,\ 9,\ 14\). A take-away pattern shrinks because you subtract the step each time, like \(24,\ 20,\ 16\).