Patterns — Study Notes for PSTET Paper I

Overview

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.

Formulas / Key Facts

| Pattern Type | Common Rules | Example | |--------------|--------------|---------| | Skip counting by 2 | +2 | 2, 4, 6, 8, 10 | | Skip counting by 5 | +5 | 5, 10, 15, 20 | | Odd numbers | 2n – 1 (or +2 starting from 1) | 1, 3, 5, 7, 9 | | Even numbers | 2n (or +2 starting from 2) | 2, 4, 6, 8, 10 | | Square numbers | n² | 1, 4, 9, 16, 25 | | Triangular numbers | n(n+1)/2 | 1, 3, 6, 10, 15 | | Doubling | ×2 | 1, 2, 4, 8, 16 | | Halving | ÷2 | 64, 32, 16, 8, 4 |