The idea, step by step
Find the step from known neighbours
For 8, 12, □, 20, use the first two numbers to find the add-4 rule. Add 4 to 12 to get 16. Then check that 16 + 4 gives the next shown number, 20.
Work backwards when needed
If the beginning is missing, undo the rule. In □, 17, 22, 27, the forward step is add 5. Work backwards from 17 by subtracting 5. The first number is 12.
A common trap
Filling a gap with any number between its neighbours.
Instead: The rule gives an exact step. Check the distance from the previous number and to the next one.
See the thinking
A missing middle
Fill the gap: 30, 27, □, 21.
- The step is subtract 3.
- 27 − 3 = 24; check 24 − 3 = 21.
A missing start
Fill the gap: □, 18, 20, 22.
- The forward step is add 2.
- Work backwards: 18 − 2 = 16.
Check your understanding
Fill the gap: 5, 10, □, 20.
Show answer
15
Add 5 each time; 10 + 5 = 15 and 15 + 5 = 20.
Your turn
6 questions · Work at your own pace.
Read the questions online
- Fill the gap: 2, 4, □, 8.
- Fill the gap: 50, 40, □, 20.
- Fill the gap: □, 11, 14, 17.
- Fill both gaps: 7, 12, □, □, 27.
- Fill the gap: 36, 32, □, 24.
- Rui puts 19 in 10, 13, 16, □, 22. Show two checks.
Read the worked solutions
- Fill the gap: 2, 4, □, 8.
4 + 2 = 6; 6 + 2 = 8.
6 - Fill the gap: 50, 40, □, 20.
40 − 10 = 30; 30 − 10 = 20.
30 - Fill the gap: □, 11, 14, 17.
The rule is add 3, so 11 − 3 = 8.
8 - Fill both gaps: 7, 12, □, □, 27.
Add 5 at every step.
17, 22 - Fill the gap: 36, 32, □, 24.
Subtract 4 at each step.
28 - Rui puts 19 in 10, 13, 16, □, 22. Show two checks.
The missing value follows the same rule on both sides.
16 + 3 = 19 and 19 + 3 = 22.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Constant increases/decreases; describing rules; missing terms; shape/number patterns.
Official curriculum source ↗