Number & Algebra
Number Patterns and Rules
Year 3 · Year 4
- ✓By the end of this lesson students will be able to identify and describe simple number patterns.
- ✓By the end of this lesson students will be able to determine the rule for a given number pattern.
- ✓By the end of this lesson students will be able to extend number patterns using their identified rule.
- ✓By the end of this lesson students will be able to create their own number patterns given a starting number and a rule.
Key concepts
A number pattern is a list of numbers that follows a special order or rule. Each number in the pattern is called a 'term'. Patterns can be 'ascending' (going up, getting bigger) or 'descending' (going down, getting smaller).
The 'rule' of a number pattern tells you exactly how to get from one number to the next. To find the rule, look at the difference between consecutive numbers. Ask yourself: Am I adding, subtracting, or skip counting by a certain number to get to the next term? For example, in the pattern 2, 4, 6, 8, ... the rule is 'add 2'.
Once you have found the rule, you can use it to find the next numbers in the pattern. This is called 'extending' the pattern. You just keep applying the rule to the last number you have.
You can create your own number patterns! All you need is a starting number and a rule. For example, if your starting number is 5 and your rule is 'add 3', your pattern would be 5, 8, 11, 14, ...
Key facts to remember
- 1A number pattern is a sequence of numbers that follows a predictable rule.
- 2The 'rule' tells you how to get from one number to the next in the pattern.
- 3Patterns can be ascending (numbers increase) or descending (numbers decrease).
- 4To find the rule, look at the difference between consecutive numbers.
- 5Always check that your rule works for all the numbers given in the pattern.
- 6Skip counting is a common way to create number patterns (e.g., skip counting by 2s, 5s, 10s).
- 7The '...' (ellipsis) means the pattern continues in the same way.
Worked examples
Example 1
Identify the rule and find the next two numbers in the pattern: 7, 10, 13, 16, ...
Answer
Rule: Add 3. Next two numbers: 19, 22.
This is an ascending pattern because the numbers are getting bigger.
Example 2
What is the rule for the pattern 40, 35, 30, 25, ...? Then, write the next three numbers.
Answer
Rule: Subtract 5. Next three numbers: 20, 15, 10.
This is a descending pattern because the numbers are getting smaller.
Example 3
A pattern starts with 6 and the rule is 'add 4'. Write the first five terms of this pattern.
Answer
The first five terms are: 6, 10, 14, 18, 22.
This pattern is also known as skip counting by 4, starting from 6.
Common mistakes
- ✗Only checking the rule for the first two numbers and not verifying it for the rest of the pattern.
- ✗Making calculation errors when adding or subtracting to find the next terms.
- ✗Confusing the operation (e.g., thinking it's 'add 2' when it's actually 'subtract 2').
- ✗Not reading the question carefully and providing too many or too few next terms.
Exam tips
- ★Always find the rule first and write it down clearly.
- ★Double-check your calculations, especially when extending the pattern.
- ★If the pattern is long, write out each step to avoid errors.
- ★Pay attention to whether the pattern is increasing or decreasing to help determine if the rule involves addition or subtraction.
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