The idea, step by step
Compare neighbours
Look at two neighbouring numbers to find the change. In 12, 17, 22, 27, each number is 5 more. Check more than one pair before choosing the rule.
A pattern can go backwards
The numbers 60, 50, 40, 30 decrease by 10. Continue by taking away another 10. Keep the direction as well as the step size: add 10 and subtract 10 are different rules.
A common trap
Choosing a step from just one pair when later steps do not match.
Instead: Test the rule between each pair shown. A constant-step pattern must use the same change each time.
See the thinking
An increasing pattern
Continue 14, 17, 20, 23 with two more numbers.
- Each step adds 3.
- 23 + 3 = 26; 26 + 3 = 29.
A decreasing pattern
Continue 45, 40, 35 with two more numbers.
- Each step subtracts 5.
- 35 − 5 = 30; 30 − 5 = 25.
Check your understanding
What is the next number: 22, 24, 26, 28?
Show answer
30
Add 2 each time.
Your turn
6 questions · Work at your own pace.
Read the questions online
- Write the next two numbers: 3, 6, 9, 12.
- Write the next two numbers: 40, 35, 30.
- What is the step in 16, 26, 36, 46?
- What is the step in 18, 16, 14, 12?
- Continue 90, 80, 70 with one more number.
- Is 5, 10, 15, 21 an add-5 pattern all the way? Explain.
Read the worked solutions
- Write the next two numbers: 3, 6, 9, 12.
Add 3 twice.
15, 18 - Write the next two numbers: 40, 35, 30.
Subtract 5 twice.
25, 20 - What is the step in 16, 26, 36, 46?
26 − 16 = 10, and the later steps match.
Add 10. - What is the step in 18, 16, 14, 12?
Each number is 2 smaller.
Subtract 2. - Continue 90, 80, 70 with one more number.
70 − 10 = 60.
60 - Is 5, 10, 15, 21 an add-5 pattern all the way? Explain.
15 + 5 would be 20, not 21.
No. The final step adds 6.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Constant increases/decreases; describing rules; missing terms; shape/number patterns.
Official curriculum source ↗