Patterns form a foundational topic in primary mathematics, helping children recognise regularity, predict what comes next, and develop early algebraic thinking. In PSTET Paper I, questions on patterns test your ability to identify, extend, and create both number patterns and shape patterns appropriate for Classes I–V.
This topic bridges arithmetic and geometry. Students learn to observe repetition in numbers (skip counting, odd-even sequences, growing/shrinking patterns) and in shapes (repeating units, symmetry, tessellations). Mastering patterns also supports problem-solving skills because children learn to generalise rules — a precursor to understanding variables and functions later.
For the exam, expect 2–4 questions that ask you to find the next term, identify the rule, spot errors in a given pattern, or answer pedagogy-based questions on how to teach patterns effectively.
Key Concepts
**Repeating pattern**: A sequence where a core unit repeats unchanged (e.g., red-blue-red-blue or ▲○▲○). The smallest repeating unit is called the "pattern unit" or "core."
**Growing pattern**: A sequence where each term increases by a fixed rule (e.g., 2, 4, 6, 8 — add 2 each time). Also called an "increasing pattern."
**Shrinking pattern**: A sequence where each term decreases by a fixed rule (e.g., 20, 17, 14, 11 — subtract 3 each time).
**Number pattern**: Any sequence of numbers following a rule — includes skip counting, multiplication tables, squares, triangular numbers, and Fibonacci-type patterns at higher primary levels.
**Shape/Geometric pattern**: A sequence using shapes, colours, sizes, or orientations that follow a rule. Includes rotational and reflective arrangements.
**Rule of a pattern**: The underlying instruction that generates successive terms (e.g., "add 5," "double and subtract 1," "rotate 90° clockwise").
**Predicting and extending**: Using the rule to find terms beyond those given — a key skill tested in exams.
**Creating patterns**: Designing one's own pattern following a self-chosen rule — important in pedagogy for developing creativity.
1. The first step in solving any pattern question is to find the difference (or ratio) between consecutive terms. 2. If differences are constant → arithmetic pattern (add/subtract rule). 3. If differences themselves form a pattern → second-level pattern (e.g., +1, +2, +3, +4). 4. Shape patterns often use rotation (90°, 180°) or reflection (flip horizontal/vertical). 5. Colour or object patterns at primary level usually have a core of 2–4 items.
Worked Examples
**Example 1 — Number Pattern (Arithmetic)**
*Find the next two terms: 7, 12, 17, 22, _____, _____*
1. **Stopping at one difference**: Students compute only the first pair of differences and assume the rule. *Correct fix:* Always check at least 3–4 consecutive differences to confirm the rule is consistent.
2. **Ignoring second-level differences**: When first differences are not constant, students panic. *Correct fix:* Compute differences of differences; if those are constant, use them to extend.
3. **Miscounting the core in shape patterns**: Picking only part of the repeating unit (e.g., mistaking ▲○ as the core when it is actually ▲○○). *Correct fix:* Write out the sequence and mark where exact repetition begins; the stretch before that mark is the core.
4. **Confusing "term number" with "term value"**: Especially in pedagogy questions, mixing up the position (1st, 2nd, 3rd) with the actual number in the sequence. *Correct fix:* Use n for position and aₙ for value; keep them labelled separately.
5. **Applying the rule backwards when shrinking**: Subtracting instead of adding when the pattern is decreasing — or vice versa. *Correct fix:* Note explicitly whether the pattern grows or shrinks before calculating.
Quick Reference
**Arithmetic pattern**: Constant difference between terms.
**Second-level pattern**: Differences themselves follow a pattern.
**Core of repeating pattern**: Smallest unit that repeats.
To find the rule: compute consecutive differences first.