PSLE Mathematics Learning Guide · Guide 22
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A pattern is more than a list that “looks regular”. A useful mathematical pattern has a rule that connects one term, stage or arrangement to another. The learner’s job is to identify what changes, what remains fixed and whether the same rule continues.
This guide uses one habit: write the terms or stages clearly, compare consecutive steps, test the proposed rule more than once, then use the rule to predict or recover a missing value.
The current Primary Mathematics curriculum includes pattern recognition and generalisation across the primary years. The MOE Primary Mathematics syllabus updated October 2025 provides the curriculum context; the SEAB 2026 PSLE examination-format page links the current Mathematics syllabus. All examples here are original eduKate teaching material.
Start by checking differences
Sequence: 5, 9, 13, 17, …
Each term increases by 4. The next term is 21.
Do not stop after checking only one jump. Compare 5→9, 9→13 and 13→17. The same +4 rule holds repeatedly.
Some patterns scale rather than add
Sequence: 3, 6, 12, 24, …
Each term doubles. The next term is 48.
A learner who looks only at differences sees +3, +6, +12. Those differences themselves change. Multiplicative patterns need a ratio or scale check as well as a difference check.
Some patterns alternate between rules
2, 5, 4, 7, 6, 9, …
The pattern alternates +3, −1, +3, −1.
Another way to see it is two interwoven sequences: 2,4,6,… and 5,7,9,…
When one simple repeated rule fails, inspect odd-position and even-position terms separately.
Growing picture patterns can be counted by stage
Suppose Stage 1 uses 4 tiles, Stage 2 uses 7, Stage 3 uses 10, Stage 4 uses 13.
The total increases by 3 tiles each stage. Stage 8 uses 4 + 7×3 = 25 tiles.
This can be written as a start value plus repeated growth. The exact algebraic form is less important than preserving the stage relationship.
Term number and term value are different quantities
For 4, 7, 10, 13, 16, … the fifth term has value 16.
The number 5 is the position; 16 is the term value.
Confusing them creates errors when a question asks “Which term is 34?” rather than “What is the 10th term?”
Work backwards when the target term value is known
Pattern: 6, 11, 16, 21, …
Each term increases by 5. Which term is 41?
From 6 to 41 is an increase of 35, which is seven jumps of 5. Seven jumps after Term 1 leads to Term 8.
Check: Term 8 = 41.
A stage table can reveal the structure
| Stage | Number of objects | Change |
|---|---|---|
| 1 | 5 | — |
| 2 | 8 | +3 |
| 3 | 11 | +3 |
| 4 | 14 | +3 |
Tables are useful when a visual pattern hides the numerical progression.
Main worked workshop: fourteen original pattern tasks
1.
7, 12, 17, 22, …
Next: 27.
2.
40, 35, 30, 25, …
Next: 20.
3.
2, 6, 18, 54, …
Next: 162.
4.
81, 27, 9, 3, …
Next: 1.
5.
3, 8, 7, 12, 11, 16, …
Rule: +5, −1 alternating. Next: 15.
6.
5, 10, 7, 14, 11, 22, …
One view: ×2, −3 alternating. Next: 19.
7.
Stage totals 4, 9, 14, 19. Find Stage 10.
Answer: 4 + 9×5 = 49.
8.
Pattern 12, 18, 24, 30. Which term is 60?
Answer: Term 9.
9.
Pattern 100, 90, 80, … Find Term 12.
Answer: 100 − 11×10 = −10. If the context disallows negatives, the pattern may stop before then; context matters.
10.
1, 4, 9, 16, 25, …
Observation: square numbers 1²,2²,3²,4²,5². Next: 36.
11.
2, 5, 10, 17, 26, …
Differences: +3,+5,+7,+9. Next difference +11, so next term 37.
12.
A learner says 2,4,8,16 continues by +2,+4,+8, so next +10.
Repair: A simpler consistent rule is ×2 each time, so next term 32.
13.
Stage 1 has 6 matchsticks; each new stage adds 4. How many in Stage 15?
Answer: 6 + 14×4 = 62.
14.
A pattern has Term 1 = 9 and adds 7 each step. Which term is 58?
Answer: 58−9=49=7 jumps; therefore Term 8.
A rule must survive more than one transition
From 2 to 4, both +2 and ×2 work. The next term distinguishes them. If the sequence is 2,4,8, the ×2 rule survives while +2 does not.
Do not declare a rule from one transition only.
Context can constrain the pattern
A seating pattern cannot have negative chairs. A tile pattern may grow only while space remains. A sequence generated in a pure number exercise may continue indefinitely.
Pattern rules describe the data given; real contexts may impose additional boundaries.
Independent transfer check
- 11, 15, 19, 23, …
- 64, 32, 16, 8, …
- 2, 7, 6, 11, 10, 15, …
- Stage totals are 3, 8, 13, 18. Find Stage 12.
- Pattern 9, 14, 19, 24. Which term is 49?
- Explain why checking only the first two terms is not enough to prove a rule.
Independent-check answers
1. 27.
2. 4.
3. 14.
4. 3+11×5=58.
5. Term 9.
6. Several rules can fit one transition; a valid rule should explain the repeated structure across multiple terms.
Parent and tutor guide
Ask the learner to write the changes between terms. If those changes are not constant, check multiplication or alternating rules. For visual patterns, use a stage table.
When the learner predicts a rule, ask them to use it on two or three transitions, not only one.
The learner’s final card
What changes from one term to the next? Is the change additive, multiplicative or alternating? Does my rule work more than once? Am I finding a term value or a term position?
Continue through the PSLE Mathematics Learning Guide
Use Guide 21: Percentage Change and Discount. Continue with Guide 23: Symmetry and Guide 24: Coordinates and Grid Position.
Return to the PSLE Learning Guide.
Sources and boundaries
Official references: SEAB 2026 PSLE formats and MOE Primary Mathematics syllabus, updated October 2025.
Teaching boundary: All examples are original eduKate teaching material. Pattern tasks are treated as cumulative Primary Mathematics reasoning relevant to PSLE preparation.