How should Primary 1–6 pupils solve number patterns in 2027? Look at differences, repeated groups, multiplication, square numbers and relationships between positions. A pattern is not solved simply by guessing the next number; the pupil should state a rule, test it against all given terms and recognise that a short sequence can sometimes fit more than one rule. This guide provides forty original worked number-sequence exercises and independent extensions.
These are general Mathematics reasoning activities consistent with MOE’s problem-solving emphasis, not a claim that every sequence type is prescribed at every primary level or will appear in the 2027 PSLE. Use P1–P2 patterns as playful number-sense tasks and select advanced sequences only when the child has learned the prerequisites. Standard and Foundation P5–P6 scope differs.
- Calculate differences between adjacent terms.
- Check whether differences themselves form a pattern.
- Test multiplication and division relationships.
- Consider position numbers and visual representations.
- Verify the proposed rule against all shown values.
- Acknowledge ambiguity when several rules fit the same few terms.
P1–P2: ten worked sequences
Each sequence has a natural simple rule, but four terms alone do not mathematically prove a unique continuation. For classroom practice, assume the simplest stated rule unless the question gives another constraint. Pupils should explain their reasoning rather than only supply the next term.
1. 2, 4, 6, 8, …
Working: The successive differences are 2, 2, 2. Simple rule: Add 2 each time. Next term under that rule: 10.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 10, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
2. 5, 10, 15, 20, …
Working: The successive differences are 5, 5, 5. Simple rule: Add 5 each time. Next term under that rule: 25.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 25, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
3. 1, 3, 5, 7, …
Working: The successive differences are 2, 2, 2. Simple rule: Add 2 each time. Next term under that rule: 9.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 9, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
4. 10, 9, 8, 7, …
Working: The successive differences are -1, -1, -1. Simple rule: Add -1 each time. Next term under that rule: 6.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 6, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
5. 3, 6, 9, 12, …
Working: The successive differences are 3, 3, 3. Simple rule: Add 3 each time. Next term under that rule: 15.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 15, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
6. 4, 8, 12, 16, …
Working: The successive differences are 4, 4, 4. Simple rule: Add 4 each time. Next term under that rule: 20.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 20, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
7. 20, 18, 16, 14, …
Working: The successive differences are -2, -2, -2. Simple rule: Add -2 each time. Next term under that rule: 12.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 12, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
8. 7, 14, 21, 28, …
Working: The successive differences are 7, 7, 7. Simple rule: Add 7 each time. Next term under that rule: 35.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 35, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
9. 11, 13, 15, 17, …
Working: The successive differences are 2, 2, 2. Simple rule: Add 2 each time. Next term under that rule: 19.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 19, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
10. 2, 5, 8, 11, …
Working: The successive differences are 3, 3, 3. Simple rule: Add 3 each time. Next term under that rule: 14.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 14, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
P3–P4: ten worked sequences
Each sequence has a natural simple rule, but four terms alone do not mathematically prove a unique continuation. For classroom practice, assume the simplest stated rule unless the question gives another constraint. Pupils should explain their reasoning rather than only supply the next term.
11. 1, 4, 7, 10, …
Working: The successive differences are 3, 3, 3. Simple rule: Add 3 each time. Next term under that rule: 13.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 13, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
12. 3, 7, 11, 15, …
Working: The successive differences are 4, 4, 4. Simple rule: Add 4 each time. Next term under that rule: 19.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 19, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
13. 2, 6, 10, 14, …
Working: The successive differences are 4, 4, 4. Simple rule: Add 4 each time. Next term under that rule: 18.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 18, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
14. 100, 90, 80, 70, …
Working: The successive differences are -10, -10, -10. Simple rule: Add -10 each time. Next term under that rule: 60.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 60, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
15. 5, 11, 17, 23, …
Working: The successive differences are 6, 6, 6. Simple rule: Add 6 each time. Next term under that rule: 29.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 29, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
16. 1, 5, 9, 13, …
Working: The successive differences are 4, 4, 4. Simple rule: Add 4 each time. Next term under that rule: 17.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 17, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
17. 12, 18, 24, 30, …
Working: The successive differences are 6, 6, 6. Simple rule: Add 6 each time. Next term under that rule: 36.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 36, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
18. 2, 7, 12, 17, …
Working: The successive differences are 5, 5, 5. Simple rule: Add 5 each time. Next term under that rule: 22.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 22, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
19. 50, 45, 40, 35, …
Working: The successive differences are -5, -5, -5. Simple rule: Add -5 each time. Next term under that rule: 30.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 30, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
20. 8, 16, 24, 32, …
Working: The successive differences are 8, 8, 8. Simple rule: Add 8 each time. Next term under that rule: 40.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 40, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
P5: ten worked sequences
Each sequence has a natural simple rule, but four terms alone do not mathematically prove a unique continuation. For classroom practice, assume the simplest stated rule unless the question gives another constraint. Pupils should explain their reasoning rather than only supply the next term.
21. 1, 4, 9, 16, …
Working: The successive differences are 3, 5, 7. Simple rule: Successive differences are 3, 5, 7, changing by 2; the next difference is 9. Next term under that rule: 25.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 25, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
22. 2, 6, 12, 20, …
Working: The successive differences are 4, 6, 8. Simple rule: Successive differences are 4, 6, 8, changing by 2; the next difference is 10. Next term under that rule: 30.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 30, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
23. 3, 8, 15, 24, …
Working: The successive differences are 5, 7, 9. Simple rule: Successive differences are 5, 7, 9, changing by 2; the next difference is 11. Next term under that rule: 35.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 35, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
24. 1, 8, 27, 64, …
Working: The successive differences are 7, 19, 37. Simple rule: A possible continuation uses the last observed difference, but further terms or a stated rule are required to decide uniquely. Next term under that rule: 101.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 101, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
25. 2, 4, 8, 16, …
Working: The successive differences are 2, 4, 8. Simple rule: Multiply by two each time. Next term under that rule: 32.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 32, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
26. 5, 10, 20, 40, …
Working: The successive differences are 5, 10, 20. Simple rule: Multiply by two each time. Next term under that rule: 80.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 80, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
27. 1, 3, 6, 10, …
Working: The successive differences are 2, 3, 4. Simple rule: Successive differences are 2, 3, 4, changing by 1; the next difference is 5. Next term under that rule: 15.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 15, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
28. 2, 5, 9, 14, …
Working: The successive differences are 3, 4, 5. Simple rule: Successive differences are 3, 4, 5, changing by 1; the next difference is 6. Next term under that rule: 20.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 20, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
29. 4, 9, 16, 25, …
Working: The successive differences are 5, 7, 9. Simple rule: Successive differences are 5, 7, 9, changing by 2; the next difference is 11. Next term under that rule: 36.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 36, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
30. 3, 6, 12, 24, …
Working: The successive differences are 3, 6, 12. Simple rule: Multiply by two each time. Next term under that rule: 48.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 48, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
P6: ten worked sequences
Each sequence has a natural simple rule, but four terms alone do not mathematically prove a unique continuation. For classroom practice, assume the simplest stated rule unless the question gives another constraint. Pupils should explain their reasoning rather than only supply the next term.
31. 2, 5, 10, 17, …
Working: The successive differences are 3, 5, 7. Simple rule: Successive differences are 3, 5, 7, changing by 2; the next difference is 9. Next term under that rule: 26.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 26, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
32. 1, 4, 9, 16, …
Working: The successive differences are 3, 5, 7. Simple rule: Successive differences are 3, 5, 7, changing by 2; the next difference is 9. Next term under that rule: 25.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 25, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
33. 3, 7, 13, 21, …
Working: The successive differences are 4, 6, 8. Simple rule: Successive differences are 4, 6, 8, changing by 2; the next difference is 10. Next term under that rule: 31.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 31, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
34. 1, 2, 4, 7, …
Working: The successive differences are 1, 2, 3. Simple rule: Successive differences are 1, 2, 3, changing by 1; the next difference is 4. Next term under that rule: 11.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 11, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
35. 2, 3, 5, 8, …
Working: The successive differences are 1, 2, 3. Simple rule: Successive differences are 1, 2, 3, changing by 1; the next difference is 4. Next term under that rule: 12.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 12, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
36. 10, 13, 19, 28, …
Working: The successive differences are 3, 6, 9. Simple rule: Successive differences are 3, 6, 9, changing by 3; the next difference is 12. Next term under that rule: 40.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 40, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
37. 1, 4, 10, 20, …
Working: The successive differences are 3, 6, 10. Simple rule: A possible continuation uses the last observed difference, but further terms or a stated rule are required to decide uniquely. Next term under that rule: 30.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 30, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
38. 2, 6, 18, 54, …
Working: The successive differences are 4, 12, 36. Simple rule: Multiply by three each time. Next term under that rule: 162.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 162, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
39. 1, 5, 14, 30, …
Working: The successive differences are 4, 9, 16. Simple rule: A possible continuation uses the last observed difference, but further terms or a stated rule are required to decide uniquely. Next term under that rule: 46.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 46, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
40. 4, 7, 13, 22, …
Working: The successive differences are 3, 6, 9. Simple rule: Successive differences are 3, 6, 9, changing by 3; the next difference is 12. Next term under that rule: 34.
Explain the operation in words and test it against each pair of consecutive values. If a rule works for only the last pair, it is not sufficient. For a pattern of squares or changing differences, draw blocks or use a table of position numbers to make the structure visible.
Independent challenge: Continue the selected rule for two more terms beyond 34, then work backwards to recover the original first term. Create a new four-term sequence using a related rule and ask someone else to justify its continuation. Discuss whether a different, more complicated rule could also fit the four given values, and why a clearly stated rule removes ambiguity.
Why a sequence may not have a unique answer
Any finite list of numbers can be continued in multiple ways. For example, 2, 4, 6, 8 naturally suggests adding two, but a more complicated mathematical rule can match those four values and give a different fifth term. In school practice, look for the intended simple pattern, but avoid claiming that the numbers alone logically force only one answer. When the task states ‘add two each time’, the rule is unambiguous.
How to use tables and drawings
A table can connect position 1, 2, 3, 4 with corresponding values and help pupils see a consistent increase. A visual pattern of squares can show why 1, 4, 9, 16 grows by successive odd numbers. Such representations connect number sense with reasoning and can be more reliable than memorising a list of answers.
Four-week pattern practice
- Week 1: counting patterns and constant differences.
- Week 2: multiplication, division and skip-counting.
- Week 3: growing differences and square-number patterns where taught.
- Week 4: mixed unfamiliar sequences, rule explanation and ambiguity checks.
Frequently asked questions
Are all forty patterns official 2027 syllabus topics?
No. They are independent reasoning exercises of different difficulty.
Can a pattern have more than one valid continuation?
Yes, unless the rule or further constraints are specified.
Should P1 pupils study quadratic sequences?
No. Use age-appropriate counting and visual patterns.
What is the best checking method?
Apply the proposed rule to every given transition.
Do these predict PSLE 2027?
No. They are original examples.
Official sources
Reviewed 13 November 2026. Original educational number patterns, not official examination questions.