A pattern is something that repeats in a regular and predictable way. Patterns are all around us — in tiles on the floor, in music, in the petals of a flower, and even in numbers!
Types of Patterns
1. Shape/Colour Patterns
Objects or colours that repeat in a fixed order.
Example: circle, square, triangle, circle, square, triangle, ...
The repeating unit here is: circle - square - triangle.
- 2. Number Patterns
- Numbers that follow a rule.
- Adding the same number each time: 2, 4, 6, 8, 10, ... (add 2 each time — even numbers)
- Subtracting: 20, 17, 14, 11, ... (subtract 3 each time)
- Multiplying: 1, 2, 4, 8, 16, ... (multiply by 2 each time)
3. Growing Patterns
Each group gets bigger by a fixed amount.
Example: 1 dot, 3 dots, 6 dots, 10 dots, ... (adding 2, then 3, then 4 — triangular numbers)
4. Tiling Patterns
Shapes that fit together without gaps or overlaps to cover a surface. Squares, rectangles, equilateral triangles, and regular hexagons can tile a flat surface.
Finding the Rule
To find the pattern rule: look at two or three neighbouring terms and ask "what was done to get from one to the next?"
Find the next number: 5, 10, 15, 20, ___
Rule: add 5 each time. Next number = 20 + 5 = 25.
Find the missing shape in: circle, triangle, circle, triangle, circle, ___
The pattern repeats every 2: circle-triangle. After circle comes triangle.
Find the next two numbers: 3, 6, 12, 24, ___
Rule: multiply by 2 each time. 24 x 2 = 48.
Find the rule and the next term: 100, 90, 80, 70, ___
Rule: subtract 10 each time. 70 - 10 = 60.
Complete the pattern: A, B, B, A, B, B, A, ___
The repeating unit is A-B-B. After A comes B.
Key Points
- Always check at least 2 steps before deciding the rule.
- A pattern must have a consistent rule that works for every step.
Common mistakes
- Students sometimes assume a pattern that works for 2 terms but not the 3rd. Always verify with 3 or more terms.
- Adding and multiplying can look similar for small numbers — check carefully.
Summary
Patterns repeat by a fixed rule. We find the rule by looking at consecutive terms. Patterns can involve shapes, colours, or numbers.